 way the formula route which we have studied. Okay, so this knowledge will be important for again building your knowledge in topics like coordinate geometry and integration and application of derivatives and things like that later on. So hence it becomes important. Now in the board exams this is an important topic why because there are 10 marks for this and this is very easy topic. All of you anyways have been doing this area volume since like what I think grade seven eight so in different formats we you know you have been applying these these formulae. So hence it should not be a big issue for you to score here but yes the problem is people do mistakes or do people make mistakes while calculating so that has to be taken care of and yes if you you know get the question wrong because you know if you understand it in a different way and you solve it if the diagrams and other things are not given then you lose marks. So hence we have to be careful and one five marker mostly will be from this topic. Okay, so hence you know stakes are high so let's say many people start from the end of the paper right toward the end of the paper question number 36 and all. So there if you're spending initial few minutes on the problems then you're you're very calm so hence ideally you should not be making mistakes but many a times this question many of you would be attempting in the last minutes of the exam or when you are finishing the paper. So at times again becomes difficult to keep control over the calculations so hence these are some points to be taken care of okay. So the topic is very easy and simple and again as I told you I will show you you know the structure of the paper so you can see again menstruation is 10 marks. Now this menstruation also includes what do you call it the circle areas and all right. So cleaner figure so you have seen the areas related to circle is also included in that. So in the sample paper which is given there are five plus one six total six marks question okay. So in the sample paper there is six marks question which is given six marks so one plus five okay. So you can imagine five plus one six from this topic and four from the other two that is the areas related to circle and plain figures and things like that. So that's the breakup and total is 10 marks so these 10 marks are very easy to score okay. Now again this has been taken away now in the last few years the five marker no I'm talking I'm talking about menstruation areas related to areas and volumes basically so where you are calculating areas of plain figures and volumes and things like that. So that will fall in geometry so circles we have already taken up we will see triangles later on. So we'll spend some good amount of time on triangles why because that's another very important topic not only with respect to words but for all your future purposes. Anyway so what I'm saying is this has been removed and in the last few years there has been a four or five marker question from this topic frustum of a cone right. So fortunately and fortunately that has been removed so now you don't need to pay attention to those questions so there will not be any question like there is a cone and there is a plane which cuts the let's say there is a plane through which you are cutting the cone like that you have cut the cone so you get a frustum so bucket kind of a structure so that is taken away so that's not there okay. Now again this is the customary slide so you know the breakup by now you must have been you must have by hearted it isn't it so what is how many how many one marker so there are 16 one marker 16 into one then 16 into one again in terms of four case studies and then six into two and then seven into three and then five into three or sorry three into five so this is the structure total structure and this this is one five marker will be mostly will be a menstruation or areas or surface areas and volume dilated question now in one slide you can complete this entire revision there is nothing much here you only need to be alert and vigilant while solving the problem that's it so you can see cuboid cube cylinders sphere hemisphere and cone one important point here is the cone and the cylinder which is talked about is a right circular cone what is it right circular so you understand what is the right circular cone right circular cone slash cylinder okay so right right right circular cone slash cylinder meaning if you uh the axis of the cylinder as well as the cone will be perpendicular to the base and it will be passing through the center of the base so that's what is meant by right circular cone and cylinder what do I mean so let me just explain so all of you are clear what is right circular cone and cylinder do I need to explain that so we in this all these formula related to right circular cone and cylinder guys yes no do you understand what is right circular cone right so do not get confused so in any ways in this grade they will not test you on that but you must be aware that what we are talking about is right circular what is that actually so let me say yeah so so basically this is a right circular cone where you have this structure and the base is this and the angle this angle so non-right circular cone I'll tell you that also so have you have you seen a spotlight in our theater okay so this is a right circular cone right so non-right circular cone is something like that have you seen that spotlight kind of a thing so in the in the theater so let's say there is a beam of there's a torch here or something and here is where so hence if you see the axis is inclined right this angle is not 90 degree theta is not equal to 90 degree this is also a cone so you can make a right circular cone into a non-right circular by doing what just cut it across like this cut it and then you will get a non-right circular cone isn't it did you understand the construction so this is okay similarly there is a right circular cylinder so you have this okay and so basically if you rotate a rectangle around any of its sides you will get you will generate a volume called a right circular cylinder so if you see this is the axis of the cylinder this is the axis and axis passes through the through both the centers and it is 90 degree to the to both the both the faces both the faces right so this is okay so this must be clear fair enough now so cuboid all of you know so what is curved and lateral surface area you know so curved surface area is if you just take away the base and the top surface if at all there isn't any then that will be called as what will that be called as that will be called as curved surface area or lateral surface area so you have to just ignore the base and the so for example coming back to this so curved surface area would be this this this this area so if you let's say unwind it or cut it open then the area which is right this is curved surface area so the base is not included the base is not counted base is not counted in curved surface area right but if it is asking total surface area then everything you have to count the curved surface area as well as the the base area okay fair so you understand what is lateral surface area or curved so if it is a continuous smooth curve then it is called curved surface otherwise lateral surface area for a cuboid for example what would be lateral surface area so if you see if I draw this cuboid or cube let's say let's say this is the sorry somewhat like that okay so this is a cuboid so lateral surface area will be this surface area one this surface area two then on the backside third and on the this side four these are lateral surface areas of the cuboid the top surface and the bottom surface is not counted so base is not counted so you have to be careful in case of cuboid why because the orientation influences the curved lateral surface area why because if let's say this is h this is b and this is l and you you know turn it 90 degrees what do I mean so if I flip it 90 degrees in turn in in this case like that so let's say now l is here l is here the longest length is here and then let's say something like that is happening okay then you have to be careful about which side you are going to take for calculation up so hence in this case the things have changed so this is l now this is let's say b only and this is h this one is h so hence again this surface area that surface area that surface area and again this front surface area all these are lateral part of lateral surface area so you have to be very very careful in terms of if at all there is a cube or a cuboid orientation does matter so take care of that okay now the formula is pretty simple you have derived it there is no derivation or asked in the exams so you know how a cuboid is twice lh plus bh and twice lb plus bh plus lh this total surface area you can calculate and do if you forget the formula you can calculate there itself lbh is the volume so you have been studying about this for a long long time so all the formula is known to everyone right so do you need to uh do I need to repeat anything here so I hope everyone is clear with whatever is there on the slide and this slide is good enough for the entire chapter right the only thing is people do get confused here so in cone you have to be a little careful that this l l is slant height so what is slant height so you know that there are two heights in the cone one is the vertical height so this is the vertical height h and this one is l and this is radius so l is clearly under root h square plus slant height we call it orientation part again yes I'm saying let's say in their question if someone is asking you to find out the lateral surface area so for a cuboid it depends on which face it is kept is it so what is the base so hence you have to first identify that base so if you change the orientation the lateral surface area changes are you getting my point so let's say if you are holding a book in your hand and let's say the flat surface is on the table then its lateral surface area is very very small but you just hold it vertically so that one of the edges is on the table then the lateral surface area changes right so depending upon on which side you have kept the um the the cuboid which face you have kept the cuboid lateral surface area will keep on changing but lateral surface area doesn't vary for sphere hemisphere or a cone right so it is understood that because lateral surface area there is nothing but the curved surface area we call it so curved surface area there's only one curved surface so hence there is no need of clarification of any orientation right so is that okay for all this is fair enough so cube 4a square 6a square a cube so I don't need to repeat all of this this will be too boring anyone want me anyone wants me to repeat this okay so here 6a square 6a square a cube 4a square 6a square a cube uh no then they would have given you something you know if you know some orientation would be there otherwise you can just take length and based on length and breadth the largest surface area and if you are let's say you're confused then do mention your assumption as I told you whenever you are in doubt let's say you find the question a little ambiguous and you think that question should have been in a different world you know it has it had to be worded differently then do mention your uh you know assumption that this is what we are assuming okay so anyway so 2 pi r h and 2 pi r h plus 2 pi r square is the total surface area why 2 pi r square because there are two surfaces top and bottom so that will be it volume pi r square h this is base area into height so you can relate to it base surface area into height then sphere is 4 pi r square is a total surface area so lateral surface area or total surface area stays the same for sphere and volume is 4 by 3 pi r cube uh hemisphere lateral surface area or curved surface area is 2 pi r square total surface area surface area add one more pi r square to the curved surface area you will get 3 pi r square the volume is half of the sphere so 2 by 3 pi r cube this one and r is the radius you know this and cone curved surface area pi rl pi rl plus pi r square is the total surface area and half 1 by 3 pi r square h so this is if you see is one third of the volume of the cylinder right and r is equal to base radius h is equal to vertical height l is equal to slant height l is under root r square plus h square so with this slide you don't need any further gain on this you have been doing so far you know multiple number of times so let's start solving but before you solve these points must be taken care of and this is where people go wrong so please be careful so let's say in problems involving melting and all where something is being melted and reshaped and you know you are creating something so volume remains constant this is the key right so the volume of the structure before doing any work on it and volume of structure after doing any work on it for example there will be case questions like eight metallic spheres were melted to form let's say two cylinders of some dimension then what is going to be constant in this process the volume is not going to change so that will be the key of the question so you have to equate the volumes to get the relation between the dimensions okay now many a times the value of pi is given so it's better to look at the question and see whether some value of pi is given some approximation is given at times so use that value only which is given in the question if nothing is given you are free to choose 22 upon 7 or 3.14 whichever you feel comfortable to do the calculation but in my opinion 22 by 7 is a better way of doing arithmetic okay so you can use 22 by 7 and many a times you have to be careful whether the value of radius or the diameter is given so people get trapped there so hence they in the in the temptation because as you know most of you would be doing these problems towards the end of the paper so it might so happen because of the rush of you know rush of solving more and more and yeah I will I will tell you that also conversion so no worries so what I'm saying is um then during the rush it might so happen that you overlooked radius and you've taken or you overlooked that it is given as diameter you took it as a took it as a radius and solve the paper solve the problem and hence got the answer wrong so in my opinion what you should do is you solve in terms of variables till the last point so hence you can see as far as possible do all the calculations at the final stages of solution so hence keep going taking r r r r like that till the end and only when you have reduced everything and now it's final you know final step where you have to calculate then you deploy values so even if let's say at the end you are you know doing the calculation which is let's say by mistake you took the diameter value as the radius then at least the process will save you right so hence we say that keep the calculations for the end okay and try to do without much of you know so you try to solve using variables you can show in the diagram draw the illustrative diagram there itself so what is r what is h what is d x y z whatever it is asked for it is asking for then solve methodically and at the last stage yes many a times you will feel that okay no it will be too much to carry on all these variables till the last then please be careful many a times it happens that you have to first calculate the volume of the cone then go to something else and all that so it becomes difficult to carry on with the variables then while deploying the values be double alert that what kind of information has been given then do not miss writing units many a times I have seen people just forgetting to write units so whether it is centimeter meter kilometer whatever is mentioned do mention the units because there is weightage on that as well okay so and someone is asking about conversion so what all conversion do you need centimeter so one meter is 100 centimeter without doubt you have been doing it is equal to 1000 centimeter okay decimeter so one meter so milli centimeter so 10 decimeter like that okay so one meter is 10 deci so these values are not not will be there so they will not give you decimeters and all that now this is unconventional anyways no one uses decimeter and decometer and all that so hectare so one hectare is how much 10,000 meter square right so this will be there and in in most of the cases you will see that they will give you this information okay so they will give you the information yeah these days I'm not seeing any questions like one feet is how much so one feet is 12 inches and one inches 2.54 centimeter like that so you can you know you can always relate to your ruler which is there in your instrument box if you see in the geometry box you'll see a ruler so there are 15 centimeter ruler and six inches on the side is it so six inches roughly equal to 15 centimeter so right so you might have seen that in here so mostly if at all there is some conversion it would be there I believe I have not seen them going away from SI units for a long time you'll see all the previous year questions so but yes it's always good to remember those values anything else okay so sir do we consider a tent to have a base see when a tent question is given they will ask you about the canvas area so obviously base will not be there you cannot create a you know so the whenever when you create a tent you do not you know consider that base in that tent okay so the question are application based where they're asking you to find out the cost of painting that or cost of fabricating that and all that so the base area is not there in the tent okay so let's proceed with the previous year questions now one by one here is the first question so this is the sample paper question so again you can see there's a melting involved in it so you know what to do here what do you need to do so you just equate the volumes is it so what is the question 12 solid cylinders of same radii are made by melting a solid metallic cylinder of base dia 2 centimeters see again so you have to be careful they are talking about base diameter diameter base dia 2 centimeter unit alert or and height 16 find the diameter of each sphere so what do you need to do equate the volume so it is a one marker so you will not write much so you'll say 12 solid spheres so 12 solid sorry meaning full right so 12 4 by 3 let's calculate the volume of the entire 12 12 solid sphere so 4 by 3 pi r cube this is the volume of 12 solid spheres is made by melting a solid metallic cylinder oh where did it go here solid metallic cylinder what is solid metallic cylinder of base diameter 2 centimeter so r here is 1 and height is 16 so hence it will be pi r square 1 square into h 16 this is the volume of the cylinder once again pi 1 square into 16 is the volume of the cylinder now what do you need to find out find the diameter of the so hence you have to find out 2 r so be careful right so hence whatever r is there you have to find out 2 r so pi pi will go so i will go so 4 4 just 16 3 4 12 4 4 right so r is simply 1 if r is 1 d is 2 r is equal to 2 and then write centimeter 2 centimeter one mark okay next so one mark done what's our target guys what are we fighting for what's the target what's the target did you do you remember the target all of you forgot it all of you have to get sent them correct so hence the quest is for sent them okay next question here guys tell you do this this is now take your time again this is five marker guys so hence please take your time read the question thoroughly and then that's all so water is flowing through a cylindrical pipe of internal diameter now the moment you see internal diameter on all that your antenna should give you signals internal diameter of 2 centimeter diameter so again trap diameter into a cylindrical tank of base radius base radius now 40 centimeter at the rate of 0.7 meter per second right so this is the velocity which is given by how much will the water rise in the tank in half an hour so draw a listed in diagram so a diagram would be something like this so this is my pipe and is water is coming to this cylindrical structure okay something like that and this is flowing at the rate of v is equal to 0.7 meter per second that is equal to 70 centimeter per second so that will be important to convert it 396 is what miles 396 is light years what is the unit by how much will water rise in the tank the answer should be in centimeters no in half an hour okay so first you will calculate the volume coming out of this pipe the output of the output of the inlet pipe inlet pipe will be nothing but what volume per second yes or no volume per second so what will that be so that is nothing but nothing but uh so let let us say that is what what should we know and keep the name as so usually we give okay some other name not v so i'm just you know trying to find out or you can just output of the inlet pipe is nothing but you can say the base area so what is the base area internal dia is two that means pi into one square base area into 70 cm cube per second this much amount of water will come down in one second so water water flown in how many half an hour 30 minutes will be equal to pi into 70 into 30 minutes means 30 into 60 centimeter cube this much water will flow down right now this is collected in the the bigger tank this one so hence the volume volume gained by the tank will be volume of water which is coming in so what is the volume gained by tank volume gained by tank is nothing but pi into base radius 40 square into let's say height h this height h only you are trying to calculate so you have to equate these two simple so hence pi into 40 square into h will be equal to pi into 70 into 30 into 60 now if you notice i did not calculate ever i'm not calculating i'm not wasting my time to calculate this value no need no need why because it is going to be simplified so if you calculate if you multiply and then you divide useless right so what are what are what else pi pi will go so this 40 square will come down as 40 into 40 is it so zero zero zero zero right now uh two three that's it right so this is how much 70 into 9 by 8 so 630 by 8 centimeter which is 87.56 70 so 8 8 just 64 60 so 756 78.75 centimeter is the answer okay so 630 upon 8 78.75 is that okay any understanding problem that you did not understand what is the what is the ask of the question what are they asking so many times understanding the problem itself becomes difficult so what are you know you are not able to always remember volume flow rate later on anyways in 11th grade you are going to study this volume flow rate in any pipe volume flow rate meaning amount of fluid passing per second the volume of fluid passing per second is nothing but area into velocity of the fluid velocity of fluid so the cross section area in which the you know the flow is happening into velocity velocity is nothing but a meter per second or yeah area of cross section so area of cross section multiplied by velocity of the fluid will give you volume flow rate of the fluid so what is the difference between volume flow rate and this velocity velocity is nothing but how much how many meters covered per second by the fluid let's say in a pipe something is flowing so in one second how many meters linear distance covered by any particle of the fluid that is velocity of the fluid but how much volume is passing through at one particular cross section area is nothing but amount of fluid passing through one particular cross section in one second and that is given by the cross section area into the velocity so that is how you will calculate how much volume is flowing in a river in the pipeline whatever next this is actual board paper so you could see in the sample paper there's one five marker and one one marker so that means total is six marks question it might vary it might become two plus three plus one maybe one plus two plus three like that so around six marks there would be one question next question here so around six marks there will be questions from areas surface areas volumes two cones have their heights in the ratio one is to three and the area in the ratio three is to one what is the ratio of their volumes it's a one mark question 1920 previous year board paper everyone is getting threes to one so in such questions two cones have their heights in the ratio so let's say h one h one by h two is one by three and radii r one by r two is equal to three by one right so what is the ratio of their volumes volume v one is one by three pi r one square into h one and v two is one by three pi r two square into h two right now divide v one by v two v one by v two will be one by three pi r one square into h one divided by one by three pi r two square into h two so one by three pi will go so r one by r two is and square so nine by one into one by three so hence three by one okay so v one by v two is threes to one so that means if the heights are in the river heights and radius are in the reverse ratio heights and radii are in the reverse ratio then the volume is in the ratio of the radii okay next this is two marks the volume of a right circular cylinder with its height they go they have mentioned right circular cylinder with its height equal to the radius is this so height is equal to radius find the height of the cylinder and pi value is 22 by 7 alisha and aditya have got the results everyone is saying two centimeter okay volume of a right circular cylinder with its height so even if it is two marks i will quickly draw our rough diagram on the sides of my answer script quickly okay so you don't need to draw for with so draw free hand so using pencil you'll be able to do better on a tablet becomes little difficult to draw beautiful diagrams anyways so r is equal to h right height is equal to the radius so h so let us say this is r and this is r both are r so what is the volume volume of a cylinder always write the formula first don't jump on to the numbers on numerals so this is nothing but pi r square into h so in this case since r is equal to h so volume will be pi r cube okay and this is equal to how much 25 1 by 7 okay so pi is 22 by 7 into r cube is equal to 25 176 176 by 7 so 7 clearly this is going to be this is divisible by 22 176 is uh how many times so 10 16 times is it no eight times eight times so 22 is eight times right so r cube is i is 2 centimeter do not forget to add the right two marks this is last year paper solid iron cuboidal block of damage i have removed all the frustum based questions right because that's not there in your syllabus for instance so solid iron cuboidal block of dimension 4.4 into 2.6 into 1 is cast into a hollow cylindrical pipe of internal radius 30 and thickness 5 find the length of the pipe four marks time taking so don't calculate the dimensions are friendly don't calculate you got it or this is the previous only find the length of the pipe 112 meter okay all of you are doing the calculations properly check check your calculations are oh my god centimeter iron can it be in centimeter you did not pay attention to the dimensions given oh different different answers are coming now i understand where where the thing is going to go yes 112 meter is the right answer looks like most yes 112 watt meter or centimeters sorry so 112 centimeter not meter so 1.12 meters no yes everybody is getting different different answer 112 meters you are getting is it oh yes yes yes sorry my bad yes 112 meters correct correct correct hashita meters yes so there go so what to do a solid iron cube first of all let's understand this hollow cylinder thing what is hollow cylinder guys so what is the what is the thing in hollow cylinder so let's say this is hollow cylinder drawing in this becomes a little difficult but anyways and then let me change the color to make it more yeah so if i yeah so this is what is a hollow cylinder okay so any pipe you see is actually a hollow cylinder because there cannot be zero thickness of any so sorry for my bad drawing because of this pen tab anyways so what is given guys this is what we found out this is not known let's say l this is not known but what all are given so this outer radius is 30 plus thickness so thickness is five only you know thickness is five so this will be 35 and inner radius is 30 right inner radius is 30 and outer radius is 35 so what is the volume of the cylinder a circular cylinder volume will be nothing but pi into 35 square minus 30 square into l this is the volume of the pipe and this is this must be equal to what whatever is the you know the solid iron cube what block was there because the volume has to be same so this will be 4.4 into 100 uh into 2.6 into 100 all in centimeter because in the left hand side i have taken so one into 100 this is what is the equation simple and then done now don't calculate 35 square and 30 square use your identity because knowledge so pi is 22 upon 7 35 square minus 30 square will be 35 minus 30 and 35 plus 30 into this l and this is how much so 440 into 260 i will deliberately keep it like that so that it becomes easier for me to do some calculations 22 gone 20 times okay what else this is five no this is five so this is four and this is 65 this 35 plus 30 is 65 so 13 five times and 13 20 times therefore making sense right and then five and four again so what is left l l is nothing but seven into four into four into 100 centimeter divided by something one has to be correct where did you go um i 30 uh um so there will be something left also so four into four okay that's it so how much 16 into 7 128 100 centimeter i'm sorry 112 112 so seven is here no this seven will come this side okay got it or or not 16 7 ah 112 112 this centimeter so this is 112 meter okay so this is the answer so annular or let's say uh cylindrical pipe volume so you can take down volume of a cylindrical pipe will be pi into r square minus r square into h where r is the outer radius outer radius and small r is inner radius right and the and the fundamental is the total volume minus the internal hollow volume you minus it subtract it you will get the volume of the pipe next question one mark spherical metal ball of radius eight centimeter is melted to make eight smaller identical balls the radius of each new ball is seven how do you divide derive total surface area of follow cylinder so total surface area of follow cylinder will be okay aditya's question here so total surface area of this thing is first outer surface area what is outer surface area oh this is 2 pi capital r into h plus internal surface area how much 2 pi small r into h plus twice the twice into pi r square minus r square this is the total surface area of a hollow cylinder hollow cylinder yes is it okay so this is outer surface this is inner surface and the top surface and below surface top surface bottom surface top surface is pi times r square minus r square and multiplied by 2 so this is a total surface area of a this thing okay this is done spherical metal ball of radius eight centimeter radius radius is meant to make eight identical balls the radius of each new ball let that be r let that be r so eight into four by three into pi into r cube is equal to four by three into pi into eight cube correct am i right folks this is the equation so this uncle will go and then r cube is equal to eight cube by two cube so r is equal to four centimeter but here centimeter was already mentioned so you could have avoided so four centimeter very good next simple ones this one now this is a tent cylindrical cylinder surmounted by a conical top cylindrical part is 2.1 meter high and conical part has slant height of 2.8 meter both the parts have same radius to find the area of the canvas simple so what is the what what are you going to calculate you are going to calculate in this case what are you going to calculate in this case total surface area of cone is it and total surface area of the cylinder correct this is the area of the canvas yes or no all right people are not saying anything lateral surface area of cylinder oh is it okay r a has already done it csa of cone plus csa of cylinder yes my dear friends oh sorry area what is 40 44 meter square so csa of cone plus all of you are saying the canvas will be csa of cone plus csa of cylinder csa of cone is pi times r times l and here 2 pi r l radius is same but l 1 and 2 are different so let's say this is l 1 l 2 okay or pi r h whichever way you want to write so pi r l 1 so pi is 22 by 7 and r is common what is r guys 2 meter so radius not diameter 2 common l 1 slant height 2.8 meters all are in meters plus pi r is gone here what will be left to into l 2 height cylindrical part height is 2.1 this one and this will be in meter square so this is 44 upon 7 into 2 into 2.1 is 4.2 4.2 into 2 plus 2.8 is 7 right meter square so you got the answer 44 meter square okay right so far so good all are easy no headache so far two cubes each of volume 125 are joined end to end find the area of the resulting cube or what area it is surface area so when they are asking surface area find out the total surface area arjun we have to find out the volume can't be in centimeter cube right so these small errors will take away a lot of so hence diagram first rough diagram is something like this so you can show so we so according to convention whichever side or edge is not visible you should draw with a dotted line so these are the hidden this thing so hence 125 so v is equal to 125 cm cube that means a cube is equal to 125 cm cube what is a show in the picture a so a is equal to 5 cm now this is nothing but 2a and this height is a only so the new surface area right so tsa now will be twice lb plus bh plus lh which is twice lb so 2a into a plus bh a square plus 2a into a and a square and what else lh 2a into a yeah so see i'm not writing any values i'm just in in keeping the variables as they are so 2a square plus a square plus 2a square 5a square so 5 into 2 10a square this is how i will write so 10 into 5 square this is equal to 250 cm square good how many if you got it correct few of you got a wrong answer okay so far so good all clear all good any trouble shouldn't be any trouble next solid toy is in the form of a hemispheric hemisphere surmounted by a right circular cone of same radius determine the volume of the toy also find the area of the colored sheet required to cover the toy so two questions are there no problem rn solve solve questions no issues where so in this diagram is not given and on top of it there is you know these values are also given root of 149 and 22 by 7 so akshita has calculated it already okay so different answers three different answers oh my internet connection is also unstable it says bye bye guys can you hear me just confirm hello yeah okay so draw the diagram first solid toy is in the form of a hemisphere surmounted by a right circular cone of same radius so it's like a ice cream kind of thing so and then on top of it there is a hemispherical okay this is a toy the height of the cone is 10 centimetre okay and the radius of the base is 7 centimetre so radius is given thank you so r r is 7 centimetre determine the volume of the toy first of all and then find the area of the colored sheet required to cover the toy has a cone is at the top hemisphere is in the form of a hemisphere surmounted by a right circular cone is this the correct diagram did you draw this diagram or is that any other possibility of any diagram same right you see it from top how does it matter upside down will change the volume will the volume change if you look it from upside down or first of all confirm this is the diagram okay so you can yes for other questions right so hence the surmounted hemispherical surrounded by a right circular cone of same radius so hence volume wise same diagram wise you please draw the other way around no problem so let me calculate it so okay if you don't want it so let me so this is what you're saying oh no hold down sorry your wish and let me okay so so this is what you are saying sir first draw this and draw this okay okay so now this is not h now it's okay this is what you wanted right a bit again so in color so this is h how much 10 centimeter right now height of the cone is 10 centimeter and the radius of the base is seven so this is r r is equal to seven centimeter very good determine the volume so volume will be volume will be simply one by three pi r square h plus two by three pi r cube this is the volume did you get that right so hence you can take pi by three common and r square common pi by three common r square common this will be h plus two r right so hence pi how much is pi 22 by 7 into 3 r square 49 and hence root over 149 is given I believe so hence h is 10 plus 2 r how much 10 plus 2 r oh for this it was given oh never mind 10 plus 2 r is how much 2 r 14 so it is 22 upon 7 into 3 into 49 into 24 cm cube let's do the calculation 7 7s are 49 3 8 ja correct so this guy is 2 into 11 into 56 correct so this is 1 1 2 1 1 2 into 11 1 1 2 into 11 which will be 2 2 plus 1 3 1 plus 1 2 and 1 1 2 3 2 1 2 3 2 centimeter cube this is the volume okay and now curved surface area so l how much will this l be so calculate l first l is under root h square plus r square so under root oh hence 10 square plus 49 1 root over 149 is given 12.2 centimeter so hence my tsa will be how much tsa will be curved surface pi r l write the formula first plus um 2 pi r square right this is so pi again common r again common l plus r sorry l plus 2 r so which is equal to 22 by 7 into r r is how much 7 into l is how much 12.2 into oh sorry plus 14 this is the value so this 7 this 7 will go so 22 into 14 16.2 see 26.2 22 into 26.2 are you all getting it so 56.4 into 11 so my value is 56.4 into 11 it is easy to multiply with 11 so it will be 4 4 6 cut 10 1 6 5 11 so 2 and 6 no oh 11 oh sorry why am i doing like that sorry 11 for the 44 66 7 55 plus 7 62 why am i getting 6 20.4 you are getting different right well something else where did i do 12 14 26.2 l r yeah 12.2 everyone is getting 576 where did i do some mistake identify the mistake t as a pi r l common 11 l plus 2 pi r square is okay so pi 22 by 7 into r r is 7 into l 12.2 into 2 r 2 r is 14 14 plus 12 26.2 so 22 into 26.256 oh sorry no this is also okay 224 26 12 oh why 56 52.4 no no this is a mistake sorry sorry sorry yeah so this is 52.4 so continuation of midnight 52.4 into 11 now okay so 44 57 centimeter square done okay thank you next these are all mechanical formula based keep applying formula rightly and then this is interesting water in a canal 6 meter wide 1.5 meter deep is flowing with speed of 10 kilometers per hour how much area will it irrigate in 30 minutes if 8 centimeters standing water is needed one second could you go back i went back yes so i told you what is volume flow rate volume flow rate is cross section area into velocity so that will be helpful to you always remember volume flow rate is that done aditya can we proceed yeah so do it volume flow rate water in a canal 6 meter wide 1 1.5 meter deep is flowing with the speed of 10 kilometers per hour mind the units here 10 kilometers per hour here it is 6 meter 1.5 meter how much area will it irrigate in 30 minutes if 8 centimeter again unit different so meter centimeter kilometer everything is there in the same question if 8 centimeter standing water is needed very big number share the values is it so big number five six two five okay let's see let's see let others also solve by the way today is the birthday of Swami Vivekananda i don't know if you know this Swami Vivekananda was born today you know Swami Vivekananda yes have you heard of him everybody oh good 12th january 1863 56.25 hectares for 4500 hectares meter square 56 different different answers are coming let me solve now okay so so what is the canal like this is the canal so here is the canal let's say this is the cross section okay and this is the cross section and water is flowing like this okay so what is given width is given no six meter wide and this is 1.5 meter deep okay water is flowing in this direction let's say at a velocity v or speed v so what is the volume flow rate volume flow rate how much water per second or per minute or whatever volume flow rate is cross section area so this is the cross section area guys this is where water is flowing through this cross section so how much is that six meters into 1.5 meters into 10 kilometers per hour so 10 kilometers per hour is nothing but 10 into 5 upon 18 meter per second okay so you can write in separately also let's say v is equal to 10 kilometers per hour so this is equal to 10 into 5 by 18 meter per second also you know the conversion right kilometer per hour 2 meter per second just multiply by 5 by 18 you must have studied in physics so now uh 6 into 1.5 is 9 so this is 2 this is 5 so volume flow rate is 25 25 meter cube per second so in one second 25 uh what is what is the IR that is TDS what is TDS akshita unmuted so this is this is in one second this much volume of water is coming okay now the meter is working so it is rather tedious so we can just do it for 30 minutes right by converting that into meters so in any way somewhere you have to convert into kilometer into meters whichever way so i do this in two minutes yes so hence now this is 25 meter cube so they see how am i doing am i doing i'm doing this way so in one second 25 meters 30 minutes how much volume in 30 minutes in 30 minutes volume will be equal to 25 into 30 into 60 meter cube okay now uh let's say now this is the plot and eight meter water standing is there right so this is height is eight meter is it it this height is eight meter so you have to find out the area right how much area will it be so simply you now know a into eight centimeter that means eight by 100 meters is equal to this 25 into 30 into 60 right so hence what is a a will be so 25 into 30 into 60 into 100 by 8 okay so now you calculate so hence what should i do four uh let hundred be there four two ja four 15 ja so this is two here so two 15 ja so 15 into 15 into 2500 so 225 answer i'm writing here 225 into 25 into 100 is it so it will be easier to calculate how so this is 900 by four into 2500 right so hence this is this is my way of calculating nothing you can do your way so 225 into 9 is 225 and how many zeros into 10 to the power four divided by four so this is nothing but four four the four five the 20 and again four five the sorry what am i saying four six seven 24.10 so 25 into 10 to the power four meters 56.25 hectares yep okay so 56.25 hectares most of you have got it yes is it okay so so what akshita was saying is you felt first calculate the akshita correct me if i'm wrong you said in uh one hour how much water so in one hour 10 kilometer 10,000 10,000 meters so in one hour one hour this is also correct actually easy also so in one hour how much water six into 1.5 into 10,000 okay so in 30 minutes half of it so in 30 minutes it will be oh writing in a very small space sorry for that so it will be half of it so 345 um am i right this is what you did right so divide 30 minutes so that means 3 into 1.5 4.5 into 10,000 so this much water and then this equal to a into 8 centimeter that is 8 by 100 did you do the same thing akshita this is what you did right so you find a from here yeah whichever way but you said 5,000 something anyways so check the calculations no problem let's go to the next one a solid is in the form of cylinder with hemispherical ends the total height of the solid is 20 and dia of dia dia of the cylinder is 7 find the total volume of the solid you can share those questions uh whichever questions we are having problem so converting right i will take i'll tell you what that is also very easy so what you can do is when you convert a right triangle into a core do this exercise at home also practical so what will happen in that case slant height is this side let's say a b c so in that case l is equal to a okay and the circumference so 2 pi r of the base is c that's it this is what happens when you you know create a cone using a right triangle right angle triangle is that okay but a must be equal to b for that matter a is equal to b so what will happen you this side goes and get adjoin to this side so when you form the cone it will be something like that that so the circumference is nothing but the hypothesis yes in such questions you have to assume r of cylinder is r of hemisphere because otherwise there could be infinitely many solutions no actually uh uh uh infinitely many because h is not fixed of cylinder yes so quickly draw the diagram it's too much only so hence this is the thing what are the same so what will be the height of cylinder below 13 mm huh diameter of the cylinder is seven yes radius is to known it's very easy problem find the total volume so total volume is nothing but volume of cylinder volume of sphere correct hemisphere plus hemisphere is one sphere is it or you can write v of cylinder plus two times v of hemisphere answer is done so the volume of cylinder is pi r square h and this will be four by three pi r q so pi r square is common h plus four by three r so pico 22 by seven lena so 22 by seven and r is how much guys r is 3.5 centimeters so i'll write seven by two so seven square by two square into h h is 13 plus four by three into seven by two so is it coming out to be in decimals okay so this seven and this seven will go so three two just six 13 times six is 78 78 plus 28 is 106 right so the calculation is here so this is equal to 22 into 7 by 4 into 106 by 6 have i done the calculations correctly guys let's check once again 6 13 6 are 78 plus 28 106 okay 106 by 6 this is what i am getting so someone has joined just so what will this be so this will go by 211 and 253 so hence here um 7 3 0 21 37 by 6 into 11 right 7 3 2 7 yes so now multiplying by 11 is easy so one eight one four am i right 30 and divide by six so 11 3 78 7 yeah and then here answer is here what is it 66 36 48 68 ja 48 and then 0.1 and then 46 6 80.16 centimeter cube okay good so all of you got it like my answer actually your answer my answer matches let's go to this now density question solid iron pole consists of this is 18 19 now we have moved to previous year last to last year any we have never we have not seen any question which is having any other unit system solid iron pole consists of a cylinder of height 220 and base dia 24 diameter again which is surmounted by another cylinder of height 60 and radius eight find the mass of the pole given that so first find out the total volume of the pole multiplied by the density you'll get the mass so i will draw a diagram for you then guys what happened in time i'm solving parallely just to see whether answers match or not anyone done r1 square so 12 square into 220 plus harsita what something 220 plus r2 square 8 square into 60 into 8 this is the answer so 3.14 into 12 square 1 4 4 into 220 calculation intensive and this is 64 into 60 into 8 grams this much so calculation so 1 4 4 3.14 1 4 4 into 220 i can do this calculation so 0 22 for the 88 22 for the 88 plus 8 96 carry 9 22 3 1 6 8 0 is the 34 488 88 plus 8 is 96 9 yeah this one and this one is 0 24 38 into 8 my god good good exercise so what is it 3.14 into so add it 0 and 8 4 12 1 6 7 7 8 15 0 12 7 7 8 15 2 2 3 5 and 3 into 8 fantastic these many grams ok g so this is i will write 22 by 7 only 22 by 7 here i'm writing then it is 0 16 41 45 28 correct 24 45 40 51 whatever am i right guys 8 0 to 16 1 40 41 4 40 wait a minute 0 16 1 8 5 the 4 8 5 the 40 44 yes yeah 284 16 0 oh my god only two people have got the answer so far so did you get guys this much i don't know whether you are doing this way so two calculation intensity hence it is four marks or different different answers are coming never mind so this is 22 into 7 4 28 0 5 66 so 9 4 0.2 right very good and now this has to be multiplied by 22 oops so much of calculation so 2 into 11 into i'm writing here 40594.2 grams so it is easier to multiply or you can do directly but i will do from 11 it is easier to do 11 come multiplication so it is uh 11 2s are 22 4s are 44 99 carry 10 6 44 into 2 oops different people are getting yes satyam i'm closer to your answer this is 0.2 okay so this is 4 12 7 you're getting 6 i'm getting 7 why anyways 2 to the 4 2 3 6 2 6 at 12 1 2 6 and 7 2 5 the 10 1 13 1 9 8 9 307 2.4 i'm getting this many grams so 8 93 kilos so only me and satyam are closer anyone else vashna vashna is also close 8 9 but it vashna is also getting 8 9 2 2 6 2.4 i just messed up somewhere maybe some calculation so this was tedious huh maybe because i multiplied by oh okay i did 22 by 7 maybe but right just a suspect if so if in such cases you have to spend time to repeat anyways where even if you have got it you know so now arain is getting some other other answer oops different different answer let me check using a calculator how much is it so 12 square let me see 12 square into 220 plus 8 square into 60 answer is this into 3.14 into 8 8 9 2 2 6 2 4 yes so those are what 8 9 2 2 6 2.4 is correct so 8 9 2 2 6 2 4 so i if you take 33.14 if i do why 22.7 then what will happen let's see 22 by 7 is there any difference 12 square into 220 should not be that much difference by the way but let me check 8 square into 60 answer into 22 into 8 divided by 7 huh yes if i take 22 by 7 i'm getting 8 9 3 0 7 4 so what i'm getting is correct with 22 by 7 so hence they are asking so better not to deviate from 3.14 i deviated from 3.14 because it was easier to calculate using 22 by 7 because 22 is 2 times 11 and multiplication by 11 is much easier so hence but anyways so all are roughly same but arain got way off what about others what about others you did not do calculations guys you you left it midway way way off yes that's something so calculations have to be very very carefully done i got half the value yes that's that's the thing so hence you have to see now you learned what is the issue in this it will take some time so in such cases they will trap you unnecessary calculations also so they should have ideally given you some multiples of 7 but there was no multiple of 7 nothing so it was real real real calculation intensive so you'll lose okay understood so in such cases do visit this calculation once again in the spare time what i told you to do okay this one this should be easy decorative block is shown which is made of two solids a cube and a hemisphere the base of the block is cube with edge 6 and the hemisphere fixed on the top has a dia 4.2 find the total surface area of the block actually will the position of this hemisphere affect the volume or the surface area if i shift that hemisphere equal thing yeah so now again it's a calculation so here you take pi is going to be 2 by 7 so meanwhile you are doing i will also start so that we can save some time the base of the block of cube is with edge 6 and the hemisphere fixed on top has a dia of 4.2 so it's diameter so you have to be taking care of that find the total surface area of the block oh people have already done so total surface area tsa so tsa will be first of all six into a square plus plus two pi r square minus pi r square am i right so one pi r square has to has to be taken away because there will the six a square will have a extra pi r square in the the interface which is there here this has to be removed and then two pi r square has to be added isn't it so this is nothing but six cube only so this will be 216 and then pi r square so pi r is 22 by 7 into r r is 2.1 so 2.1 into 2.1 this will be the tsa okay so this is 0.3 so this is nothing but um 216 plus 0.3 into so this is 22 into 36 0.63 okay so 216 plus 22366 carry 6 22 times 6 the tsa of a hemisphere is 3 by r square no no no hello guys you have to find out total surface area of the block it's not asking about yes sir but so you have to write 3 pi r square and minus pi r square right no are any may bhai this this curved surface area of this sphere is how much 2 pi r square correct only understood did you got it got it yeah so only the curved surface area has to be added the total cube and on top of it they are the dome has to be added that's it and then you have to take away pi r square so no one don't go by formula so if you go by tsa then you have to reduce remove 2 into pi r square understood if you go for the go by the formula of hemisphere tsa then you have to remove twice that circular common common area this area understood so hence uh so i have not gone by the formula i've just gone by the construction so 216 plus what what was that so this is 22366 carry 6 226 132 138 and point so this is 229.86 oh someone is getting 26 229.86 centimeter square this is the did you get this value 229.86 and then then what next is total volume so total volume will be now here you don't need to add subtract everything you just need to so do uh you know uh total volume will be v1 is equal to 6 cube and v2 is 2 by 3 into pi that is 22 by 7 into r cube so 2.1 cube you have to add these two yep so this is the total volume isn't it so this is 216 so someone is getting totally off result also never mind so 216 plus um 21 square 441 so 22 into 0.3 into 4.41 so let me write once again this is 22 into 0.3 211 by 7 is 0.3 into 21 square is 4.41 this is the value so this is 216 plus see i'm not using any additional assistance for calculation i'm just doing manipulation so 22 is 11 into 2 2 into 0.3 is 0.6 now i'll multiply this by 0.6 so 6 64.24 226 and 3 digits so it will be 2.646 so 216 plus then here 116 so 29.106 add this and done so this is nothing but 0.106 and as 9 plus 6 is 15 1 3 1 4 i'm getting something else you're getting something else i'm getting 245 point anyone got this one no anyone is no everyone is getting 235 is it volume did i make mistake then hold on recalculate 216 point 3 into 2.1 okay this is so 3s into 2.646 that's fine into 3s into 11 29.106 which 2 where where where do i need to multiply 2 oh here no oh 2 by 3s and he multiplied yeah oh okay yes i did not do this 2 by 3 thing i just added it yeah so 0.66 or thanks thanks into 0.66 so 19 216 235.2 yeah thanks aran so i did not multiply this 2 by 3 thank you for pointing out so it will be into 2 by 3 into 2 by 3 again tds calculation so be careful the way i am you know old guy you have to do carefully all the calculations so 19 19.2 it will be 19.2 so add this your answer is 235.2 around this so 404 or similar this will be okay no problem so be careful these are all after sometime what is what will happen is so hence uh don't solve questions with intensive calculation back to back the mind becomes saturated so hence you can if let's say you know try this either at a very fresh mind or somewhere in the middle end meto be extra cautious and hence you have to spare some time to come back and revise there will be errors so always remember so let's see how many are of different types varieties now so these are the different varieties which we have gathered anyways hello uh let me see if we have different types a cone of height 24 and radius 6 is made up of modeling clay a child reshapes it in the form of a sphere huh you can do this find the radius of the sphere and hence find the surface area of this sphere look quickly this is small two marks reshaping means volume stays constant cone of height 24 centimeter radius of base 6 centimeter is made up of modeling clay a child reshapes so what is the volume uh 1 by 3 into pi into r square into 24 and this is uh recast into a sphere so sphere will be so this is vc 4 by 3 pi r q you have to find out the what find the radius and the total surface area so vc is equal to vs so 1 by 3 into pi into 6 square into 24 is equal to 4 by 3 into pi into r q so pi and pi and 3 and 3 and 4 and 6 will go so r is equal to 6 centimeter okay the tan surface area of this sphere so surface area 4 pi r square 4 into 22 by 7 into 36 correct oh okay so how to do it um 4 into 2 is 8 8 into 6 so 11 into 8 6 of 48 288 divide by 7 so this is nothing but somewhere around 4 1 point uh 1 so 1 and 4 so 11 times this so 44 11.54 452 point so anyways okay so this is centimeter five six five seven five four different people are getting different different values oh did you round it off similar question volume flow rate farmer connects a pipe of internal diameter 20 centimeter from a canal into a cylindrical tank in his field which is 10 meter in dia and 2 meter deep oh if water flows through the pipe at the rate of three kilometers per hour in how much time will the time be filled somewhere there okay do this one board 2019 again so you're you're seeing either there's a toy either there is a melting of stuff or there is a water flow rate and things like that these are the typical questions once the cone and frustum thing has been removed three varieties so there will be a toy or there will be a remelting recasting of something or cross section area so you have to draw the diagram also let's say so this is the dia 20 centimeter so this is 20 okay cylindrical tank in his field um so this is a cylindrical tank this is two meter deep and which is 10 meter in dia so this is five meters this is five and this is 20 centimeter in dia so this is tensing right so hence okay so everybody's getting some value six seconds so let me see so in uh what is it saying rate of three kilometers per hour right so in one hour how much volume will come out in one hour in one hour how much volume will come out 3000 meters into cross section area that is pi into uh 10 centimeter so 0.1 square this is in one hour this much meter cube water will flow how this is the speed this is the surface area pi into point one right now uh to fill this volume so what is the target volume target volume to tank tank volume is how much this much pi into five meter right so five square into two this is the target volume now this must be equal to uh these divided by this 3000 into pi into 0.1 square hours is the time did you all get this part time is total volume to be filled how much four pi square into two divided by in one hour how much it is filling so how much it is filling 3000 meters into pi into point one square am i right folks so pi and pi will go so what is this these many hours matlab uh 25 um 25 into two so 25 into two is 50 so 506 so one upon this will go how many times 60 times so one by 60 into 0.01 r okay so in one hour how many minutes how many minutes 60 minutes so 60 by 60 into 0.01 minutes so that means one by 0.01 minutes which is 100 minutes yes so those who are getting 100 minutes get it answered six seconds oh my god people are also getting six seconds why so so quick in six seconds the entire volume is filled no problem no problem no need to say sorry come on it happens be careful with the calculations now this is similar instead of what will you do in this case a juice seller was uh serving his customers using glasses as shown the inner eye of the cylinder cylindrical glass was five centimeter but bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass if the height of the glass was 10 centimeter find the apparent and actual capacity of the glass what is apparent capacity of the glass the volume of the cylinder right and what is the actual volume of the cylinder minus volume of the hemisphere am i right folks is it understood so in this case would you go back once here okay can we proceed okay guys so here let's let's discuss the questions out you can you solve that back at home as well because there are a few more questions left so what we'll do is in this case what is this so apparent capacity apparent what it would appear right apparent capacity is cylinder volume and actual capacity is equal to cylinder value volume minus hemisphere volume so you'll have to do this in this question let's move to the next one you can solve at home also no problem so this one how will you solve this one a girl empties a cylindrical bucket full of sand of base radius 18 centimeter and height 32 centimeter on the floor to form a conical heap of sand so this is what she is getting conical heap of sand okay if the height of this conical heap is 24 then find the slant height correct to one place of decimal so you have to be very very careful here this is what is they are asking okay if the height of the conical heap is in and find its slant height correct to one place of decimal and yes so what is the volume here volume is given bucket full of sand of base radius so what is the volume of the sand volume of sand is equal to volume of cylinder is it and what would that be so bucket full of sand of base radius 18 so pi into 18 square into 32 cm cube this is the volume of the sand okay from here you need to find out r first so now this is equal to volume of cone isn't it so 1 by 3 pi r cube sorry r square h r square into what is the height of the cone 24 is equal to volume of this thing so pi into 18 square into 32 right so pi goes and something more will go so 3 and 8 will go here 8 times 4 it is so r is nothing but 8 in 18 into 2 36 centimeter right so l is nothing but under root r square plus 24 square which is under root 24 square plus 36 square this is the thing so hence you can take something common is it so here 8 2 and yeah so this is nothing but 8 is 12 is common actually so 12 comes out here what is left 4 plus 9 so it is 12 times root of 13 so what is root 13 value 3 point how much is the root 13 so to find out root 13 so let's find root 13 so root 13 so you know how to calculate 13.00 only 1 decimal so this is 339 what is left 400 so how do we do it 6 then how much 66 times right 66 36 carry 3 396 so 4 is remaining so 3.6 so 12 into 3.6 okay so I'm writing the value is 12 into 3.6 which is 743 okay 43.2 centimeter okay fellas in such cases no 8 bar or Karlein actually because just get 2 decimal in here square rooting and then you round it off in the final answer but anyways this should be okay so fair enough so what I'm saying is these are some more questions please try them similar questions these are these are all collated from the previous till 1718 paper so all collated it is already uploaded I know I hope you're aware where these are getting uploaded guys you know you know where it is uploaded and this is the the question which was you know which we saw you see yeah so this one is 229.86 so we saw this one this particular question where is it uploaded so here I will show you so this is this is the question the way they have written see all these statements very very elaborate you know has been explained properly what are they trying to say let R be the radius of the cylinder pipe be our meters a diagram is there you can see there is a diagram good you know our illustrative diagram can always help so you can use that then radius R so see in the brackets they mentioned R so conversions done height of the tank field is 3.15 meter time taken is this rate of flow of water all that one by one by one by one by one either two fine internals so this is all given see they're first mentioned given and then solution here so this for a four marker or five marker question it deserves these these many steps so please please make sure so volume of water in tank in half hour is this much so but volume of water pass through pipe is equal to volume of water collected in tank and all that equation is written and hence how to solve getting it how to solve so this is how you have to demonstrate where it is located it is located here so if you go to here so go to this program and for all the videos you can see the videos are here session recordings so all the recordings so far till yesterday's magnetic effector what was the last yesterday magnetic correct so this is uploaded till here and then here mock papers are there and all the ppt's are here attachments when you see these are all ppt's they know these attachments so you can download from here all that all the ppt's are uploaded in the week weekly schedule so week one week two week three all the attachments will be there so these attachments will be very handy while you are revising in the final board exams you know when you are you know so hence keep them with you and use it okay so you'll have to just run through don't do so many problems only few problems only towards the board exams will be good enough so hence we have collated last three four years paper questions will be good enough for quick revision okay so you can utilize these fair enough any doubt any question so I'm assuming that once this is uploaded you will solve the rest of the remaining questions which are there and then let me know if you are facing any trouble anywhere okay so the first slide in this was useful as I told you just keep that in mind and that is good enough so this is the crux of the entire game here any other question guys any other difficulty you are facing let me know or you guys can reach out to all of us individually also okay so you know keep working hard stay calm still long way to go okay bye bye guys take care see you again bye bye bye take care