 Okay, Nishant, can you check if anyone else is joining? Okay, Gopika, welcome Gopika, can you check with Ishani whether she's joining? Okay, Ishani, Karthike and Anura were missing. Okay, no issues. So what I do is till the time you guys are here, which topic we decided I forgot it, can you tell me? I think it was volumes and surface area and volumes. So this is the first question which I'm putting in front of you. And the question is that three solid cubes dimensions three into four into five melted to form a single cube find the lateral surface area of the new cube. Let me know once you have solved the question. And this is not into because these are three cubes. So this this will be comma here. I'm just changing a few data three, four and five centimeters done. Okay, if you're not getting it then try to understand there are three solid cubes with dimension three, four and five centimeters. So volumes, volume of or let me write total volume would be equal to V1 plus V2 plus V3, which will be equal to A1 cube plus A2 cube plus A3 cube, which will be equal to three cube plus four cube plus five cube. This is nothing but 27 plus 64 plus 125. And this gives me 81 plus 125, which is sorry this is 91 plus 125, which is 216 and this total volume should be equal to volume of new cube. So which should be equal to a cube and a comes out to be equal to six. So if a is six. So it means that the side of the new cube is of length six so lateral surface area of a cube is six a square and which is six into six square, which gives me 216 centimeter square. It is asking not total surface area it is asking lateral surface area so that will be four a square why because will not take it will be four a square only four sides would be taken in a cube. So four a square means four into six square so this becomes four into 36 which will be 144. So this is your answer. See I made I just made one mistake while teaching you that I took total surface area as lateral surface area. And this means mistakes can be made by anyone if you're not reading the question properly. So you should take a leaf out of this particular mistake which I made just now and you should be able to focus that what kind of area and volume you have to find out. So look at here is question two I'm giving now and question two is a river two meter deep 45 meter wide is at a rate of three kilometer per hour find the volume of water that runs into see per minute done. Okay, go pick I'll solve this. Okay, fine. So look at here for this question. First of all, try to understand the concept what happens with the river so I will prove that this is a question of cuboid and how it is a question of cuboid. So look at here. You will see that. So this is the length of off the river. This is the width of the river. And this is the depth of the river. So it is something like cuboid. So depth has been given as 45 meters and width, sorry, and, sorry, once again, sorry, depth has been given as two meters. Width has been given as 45 meters. Now what is length. So for length there has been a data given which is three kilometer per hour. So and what I need to find I need to find volume of water per minute. So first thing which I need to convert is I need to convert this kilometer into meter because all other dimensions are in meter. Now here I have been given rate into per hour. Here I have to find out rate into per minute. So I will convert this into meter per minute. So three into 1000 it becomes meters. And if one hour is equal to 60 minutes, so I convert this 300 by 66, which gives me 50 meters per minute. So try to understand that what happens is length of the water is 50 meters per minute. So this is what in one minute if I find the length in one minute water will cover a length of 50 meters. So let me take a volume. Volume is how much? 50 into 45 into 2. So how much it comes out? So this comes out to be 100 into 45 and 100 into 45 is how much? 100 into 45 is 4500 meter cube per minute. So if question also remember that one meter cube is equal to 1000 liters. So if you have to convert this data into this answer is completely fine 4500 meter cube per minute. If the question is asking that I need to convert this data into liters, I need to multiply this with 1000 and I'll say that 44.5 and this is 10 to the power 3 here and this is 10 to the power 3 here. 4.5 into 10 to the power 6 liter per minute water is flowing in the water flowing in the sea. So this is how this question was supposed to be done. So just note it down those who have not done. Now let me go to third question. So I'm taking 3-4 questions from every topic and then I'll be solving those 3-4 questions. If you have any doubt in any question you can send me that question on the group on my number anywhere. Now look at the question. The question says that the volume of cuboid is 1536 meter cube. Its length is 16 meter and width to height ratio is 3 is to 2. You have to find out B width I'm considering as B height as H. So you have to find B and H. Just do it. Very easy question. Okay, Gopika. I don't know the answer. I'll let you know. The answer is correct Gopika. Correct. Now look at here. Volume of cuboid is length into width into height. So length has been given as 16 meter. So L is equal to 16 meter. So V I am replacing with 1536 that is equal to 16 into B into H. So B into H I can write as 1536 divided by 16. So how much it will come? This will go 9 times. So 144 and 96 is left out. So it is 6 times. So B into H is 96. Now B by H is equal to 3 by 2. So what it gives me is that B is equal to H into 3 by 2. So replace B with H here. So H into 3 by 2 multiplied by this H gives me 96. So H square is equal to 96 into 2 divided by 3. And this gives me 32 into 264. H square is 64. So H is equal to 8 centimeter. If H is equal to 8 centimeter B is equal to 8 into 3 by 2 which is 4 into 3 12 meters. So this is what your answer is. Now one more question. This is the last question of cuboid and cuboid I'll be doing and then I'll be moving to another topic. So I am writing a wall 15 meters long 30 centimeter wide and 4 meter height is made of bricks each measuring 22 centimeter multiplied by 12.5 centimeter multiplied by 7.5 centimeter. If 1 by 12 of the volume of the wall consists of mortar how many bricks are there in the wall? Just find out the answer. Should I solve this question? Did you guys get it? No Karthikeya try it once again. See meters has to be converted into centimeters. Shani I don't think so. Okay let me solve this question for you guys. And what I've done is guys I have sent 4 questions on the group WhatsApp group. How come no one is getting? Okay look at here. So volume of wall is 15 into 0.3 into 4 meters meter cube. So which is 60 into 0.3 which comes out to be 18 meter cube. This is volume of wall. Now one-twelfth of the volume of the wall consists of mortar. It means that not every part or every nook and corner of the wall is brick. Some portion of the wall has been taken by mortar also and rest all is brick. So one-twelfth of 18 meter cube is equal to 1 by 12 into 18. That comes out to be 1.5 meter cube. So volume of brick would be this is volume of mortar. Volume of brick would be 18 minus one and a half which is equal to 16.5 meter cube. Now let me find out volume of one brick as I have taken volume of this total bricks in meter cubes. Volume of one brick also I will convert it into meter cube. So this becomes 22 by 100. This becomes 12.5 by 100 and this becomes 7.5 by 100. So how much it is this is let me first this 12.5 divided by 100 is 1 by 8. There is no doubt about it. This is 2.5. So this is 3 by 40 and this is 11 by 50. So I get 11 into 3 33 and 50 into 8 is 400 400 into 40 is 16,000. So what I will do is volume of one brick comes out to be 33 divided by 1600 meter cube. So number of bricks would be equal to total volume of bricks divided by volume of one brick which is 33 into 16,000. And 16.5 divided by this gives me to 16,000 divided by 2 gives me 8,000. So number of bricks would be equal to 8,000. So this is what the answer is. Just have a look at this question. Have a look at the solution of this question guys. And after noting it down what I want you to do is I have sent you a few questions on our WhatsApp group. Question number 14 to 18 you should solve. Keep on doing guys. Question number 14 to 18. Why I am not doing question by question because we are taking a lot of time in that. So solve 4-5 questions on a clock. It will also give you a practice about your examination. Also let me know in the chat box how many of you have solved the question paper which I have given because I would like to get back that question paper by tomorrow. Which question answer you are talking about Ishani? Are you talking about question number 14? Question 15. Question 15 the answer is 26.4 kgs. Once you are done with question number 16 let me know I will solve 14 to 16 then you solve 17 and 18. Question number 14 answer is 24. Question number 15 answer is 26.4 kgs. So question number 14 2 people have given me answer that is correct. Question number 15 answer is 26.4 kgs. I am giving 2 more minutes till question number 16. Okay Ishani give me one minute I will solve till 16. You try 16. Okay let me solve question number 14 for you. So question number 14 tells me that a cylindrical bucket of 28 cm in diameter and 72 cm in height is full of water. The water is emptied into rectangular tank 76 cm long and 28 cm height. So finally what I have to do in this question is that volume of the cylinder should be equal to volume of the rectangular cuboid. So volume of cylinder is pi r square h that should be equal to length into width into height here. So if I have to this is h1 and this is h2. So if I have to find out h2 that would be pi r square h1 divided by l into b. So 22 by 7 and diameter has been given which is 28 cm. So radius is 14 into 14 and height is 72 cm divided by 66 multiplied by 28. So what I get over here is this gives me 2. So this comes out to be 22 into 28 into 72 divided by 66 into 28. And this gives me 3 this and this gone and 272 divided by 3 gives me 24 cm. So question number 14 answer is 24 cm. Now let me go to question number 15 and question number 15 is all about. So question number 15 and question number 15 tells me that 1 cm cube of cast iron weighs 21 gram. Find the weight of a cast iron pipe of length 1 cm with the bore 3 cm in which thickness of the metal is 1 cm. So what it is trying to say is that it is something like this. It's a hollow cylinder. Now what happens is I will find out the volume of this hollow cylinder and what I do is how much it is. So diameter is bore of 3 cm. So this bore is what the hollow part of this diameter of the hollow part is known as bore. So this is 3 cm. It means that this is 1.5 cm and this thickness is 1 cm. So what happens is the volume of hollow cylinder would be pi r external square h minus pi r internal square h. So I am taking pi h outside r external would be 1.5. R external would be r internal plus thickness t. So r internal is 1.5, thickness is 1. So r external comes out to be 2.5 cm. So 2.5 square is 6.25 square and 1.5 square is which is r internal is 2.25. So volume of hollow cylinder would be 22 by 7 multiplied by height which is height or length whatever this is 100 into this is 4. So it comes out to be 400 into 28 which is 8800 by 7 cm cube. Now what happens for 1 cm cube the weight is 21 grams. So for 8800 by 7 cm cube it will be 21 into 8800 by 7. So that this 3 would be gone I will get 26400 grams. If I convert it into kgs I will divide it by 1000. So let me divide it by 1000 this will give you 26.4 kgs. Now guys try to understand one thing while doing calculation see I am not converting this portion into decimals. Why I am not converting it into decimals? Because I know that this has to be multiplied by 21 and 7 is a factor of 21. So this 21 will be divided by 7 and I will get an integer number. So that is why I am not converting this particular thing into decimals. So these small things also you guys should keep in mind while solving question. First this gives me an idea or benefit in time benefit in respect of time that we conserve. Like if you convert it into decimals obviously you will take 30 seconds to do so. And then again when you multiply it with 21 it becomes a bit tedious in that sense. So what happens is you tend to lose time as well as your accuracy gets affected. So please look at these things where this 7 can be multiplied to its factor and can be converted into integer. All these things if you look at it will be beneficial while solving the question. Now let me go to question number 16. And question number 16 tells me that a cylindrical tube open at both ends is made of metal. The internal diameter of the tube always remember that internal diameter is known as internal diameter of a hollow tube hollow cylinder is also known as bore. So here it has been given our internal is 10.4 divided by 2 which gives me 5.2 centimeters. And our external has been given to me as thickness is 8 mm so 8 mm means 0.8 centimeter. So I'll add it 10.4 plus 0.8 that comes out to be 11.2 centimeters divided by 2 it gives me 5.6 centimeter. Now length is equal to 25 centimeters. So volume would be equal to V pi r external square into length minus pi r internal square into length. So take pi l common it becomes r external square minus r internal square. So pi is 22 by 7 into 25 and this is 5.6 square minus 5.2 square. Now you can solve this by two methods if you can solve it by taking it square or a square minus b square format. So I will solve it by a square into b square format. So this gives me 5.6 plus 5.2 which gives me 10.8 and this gives me 5.6 into minus 5.2 which gives me 0.4. So what I get over here is 25 into 0.4 is 10 so 22 into 10 divided by 7 into 10.8. Now is it divisible? I don't think it is divisible. So this will go one times and then 38 so 0.5 then again 3 so 4 so 1.54 I get. So what I get over here is 220 into 1.54 so which will give me nearly. Guys one mistake I have made I have to add this 0.8 into 5.2 only because thickness would be added completely. So this will not be 5.6 this will be 6 centimeters so this will be once again just I just do the changes here. So this will be pi r external minus r internal this is 22 by 7 into 25. This comes out to be 5.2 plus 0.8 is 6 square so this is 6 square minus 5.2 square. So this is nothing but 22 by 7 multiplied by 25 multiplied by 6 11.2 multiplied by 0.8. Now this is divisible by 7 so this will give you 101.6 so 22 and this is 25 into 0.8 is 20. So this is 22 into 32 22 into 4 is 44 so this is 4 and this is 70 so answer would be 704. Now solve question number 17 and 18 done question number 17 and 18. Okay I am solving question number 17 and 18 because I need to solve cylinder also sorry cone also. So question number 17 the barrel of a fountain pen cylindrical in shape is 7 centimeter long and 5 millimeter in diameter. A full barrel of ink in the pen will be used on used upon writing 330 words on an average. How many words would use up a bottle of ink containing one-fifth of a liter. So first of all let me convert it into let me find out the volume and the volume is pi r square h and pi r square h which means 22 divided by 7 diameter is 5 so radius would be 5 by 2 and h is how much h is 7. So how much I get I get and once again let me check the or this is 5 millimeter so this this has to be divided by 10 also. So this is 5 by 20 this is 5 by 20 this 7 7 gone this gives me 1 by 4 and this gives me 11 and this gives me 10. So this gives me and this again is gone by 2 so this gives me 11 by 8 centimeter cube so 11 by 8 centimeter cube is used for writing 300 words. So how many words would be written 300 words so for 1 centimeter cube how much I'll write 1 centimeter cube is 300 divided by 11 by 8. So this comes out to be 300 into 8 by 11 and see I'm not converting converting into decimal. Now one liter is equal to 1000 centimeter cube so one-fifth of a liter so one-fifth would be equal to 200 centimeter cube. So I multiply this with 200 so how much it comes and this is not 300 this is 330 so I am converting into 330. So this gives me 30 and 30 into 8 is 240 and 240 into 200 is 48000 words. I've converted into 330 just check and question number 18 is a lead pencil consists of a cylinder of wood with solid cylinder of graphite fitted into it. The diameter of the pencil is 7 centimeter the diameter of the graphite is 7 millimeter the diameter of the graphite is 1 millimeter. The length of the pencil is 10 centimeter calculate the weight of the whole pencil if the specific gravity of the wood is 0.7 gram per centimeter square and that of graphite is 2.1 gram per centimeter square. Now try to understand is specific gravity in gram per centimeter square or gram per centimeter cube as far as my knowledge is concerned it is gram per centimeter cube. So try to understand how much would be weight of graphite weight of graphite would be see what happens is pencil is like this. This is your pencil complete pencil and into it small graphite is fitted cylindrical and what happens is this diameter has been given to me as 1 millimeter. So it means that this is 0.1 centimeter or 1 by 10 centimeter. So it's this is diameter so radius would be 1 by 20 centimeter. So for graphite volume would be pi r square r graphite square and length of the pencil has been given to me as 10 centimeter. So H so this is 22 by 7 multiplied by 1 by 20 into 1 by 20 into 10 and if I multiply a specific gravity. So this will volume sorry weight would be equal to volume of the graphite into specific gravity of the graphite. So specific gravity of graphite is 2.1 gram per centimeter. So what I do is weight of graphite is I multiply here 2.1 so what I get here is 0.3. So what I get here is 22 into 3 divided by 400 which is 66 divided by 400. So how much it comes it comes out to be 33 divided by 200 grams. And now let me find out weight of the other part of the pencil. So weight of other part of pencil would be so volume of complete pencil. So that would be so this complete diameter is 7 millimeter. So for this part so it means that radius is three and a half or 0.35 centimeter and from there I will reduce this 0.05. So this gives me 0.3 centimeter. So what comes out in the aftermath of this is. So let me find out it will be pi R pencil square L minus pi R graphite square L. So I take pi L outside R pencil is 3.35 square minus 0.05 square. So this is 22 by 7 into 10 and this is 0.35 square minus 0.05 square. So how much it is this and then for weight I will multiply it with how much 0.7. So what it gives me is that this this and this is gone. This is 22 multiplied by how much so 0.35 square is 0.1225 minus 0.05 square is 0.0025. So this gives me nothing but 0.12 so 22 into 0.12. This gives me an answer of or 22 into 12 divided by 100. So this gives me 3 divided by 25 so 66 divided by 25. Now you can add 33 divided by 200 and 66 divided by 25. This is your answer. I'm not getting into too much of calculation. So this is how you have to solve cylindrical questions. I will solve two questions of cone and then finish up the class today. The first question which I'm giving now is a cone has a height 8 meter. Cobb surface area is equal to 188.4 meter square. Find the volume of the cone. This question I'm giving you with the objective of, have you done this question? This is not the one moment. Let me solve this question as I have not got any answer. So the question is that Cobb surface area is equal to 188.4 meter square. What is Cobb surface area? Pi RL. And if this is my cone, then in a right circular cone, this is my L, this is H and this is R. So H square plus R square is equal to L square. So L can be written as under root H square plus R square. So I already know height as 8 meters. I don't know the radius. For that, what I'll do is I will find out Pi multiplied by R, multiplied by R square plus H square is 64. And that is equal to 188.4. So what I get over here is 22 by 7 into R, into under root R square plus 64 is equal to 188.4. So R multiplied by R square plus 64 is equal to 188.4 into 7 by 22. So how much it gives me? It gives me nearly or if you multiply it with 3.14, this will give you 60. So R into R square plus 64 is 60. So R square multiplied by R square plus 64 is equal to 60. What I do now is I write, I assume R square to be X. So in that fashion I get X multiplied by X plus 64 is equal to 60. X square plus 64 X minus 60 is equal to 0. So it gives me, sorry, the 60 square this will be because I'm taking square on both the sides. So I'll write 3600 here. So X square and this will give me plus 100 X minus 36 X minus 3600 is equal to 0. So X X plus 100 minus 36 X plus 100 is equal to 0. So X minus 36 and X plus 100 is equal to 0. So X comes out to be 36 and that is equal to R square. So R comes out to be 6 and X comes out to be minus 100 that is equal to R square. Square can never be negative. So this is negative. So R comes out to be 6. So your volume would be 1 by 3 pi R square H. So 1 by 3 22 by 7 or 3.14 whatever you want to take 3.14 into 36 into H is equal to 8. So this gives me nearly 1.05 and I'll get an answer as 301.44 meter square. So this is how you had to solve this question. Now one more question and then I'll wrap up the session. So the question is let me just erase it. I have to erase here also. The question is just give me a moment. Water flows at the rate of 10 meters per minute through a cylindrical 5 millimeter. In diameter. How long would it take to fill a conical vessel whose diameter at the surface 40 centimeter and depth is 24 centimeter? Just solve this question quickly. Done. Okay. So let me solve this question because I have to start a new class now. So answer of this question is a water flows at a rate of 10 meter per minute. So 5 millimeter in diameter. So how long it will it take? So volume of the water in one minute would be because water is cylindrical in nature. So volume in one minute would be pi into 0.25 square radius is 0.5 centimeters 0.5 divided by 2 is 0.25 and H is 10. So this is the volume of water per minute. And volume of cone would be 1 by 3 pi. And that is why I'm not converting this pi R would be how much 20 centimeter square. So 20 square H is 24. So this divided by this volume. So 1 by 3 pi 400 into 24. And this is pi multiplied by 25 square is 25, 1 by 25 is 1 by 4. So this is 1 by 4 square. So 1 by 16, I'm writing here and this is 10. So this pi and pi is 1. This gives me 8. So 3200 and multiplied by 16 divided by 10. So this gives me 320 into 16. So 320 into 16 is equal to and then divided by 60 because you are getting it in minutes. Let us convert it into whichever way you want. So this is how it is. So how much it will be? One mistake which I made here is this is in meters. So this I haven't converted. So this will be 1000 rather than 1000. So this will be nearly you can save. So I'll add two more zeros here. So divided by 100 also. So this gives me 3.2 into 16 which is nothing but 51.2 minutes. So 0.2 minutes is nothing but 51 minute and 12 seconds. So this is your answer. So thank you so much for joining the class. Let's meet some other time to discuss other questions. In case you have any doubt, you can post that doubt to me. Thank you so much.