 Fine sure. So I'm starting with surface areas and volume so In this particular chapter, we will be talking about three dimensional figures. So three dimensional figure means which has all three properties in it which are length which are length width and So which are length width and height so We will be discussing about these kind of areas. There are few these kind of Figures and wherever try to understand wherever we have Length width and height Obviously, we will talk about volume Apart from volume, we will talk about surface areas So for that matter if you are sitting with your book or Math book your math would book would be in cuboidal format So it would be something like this So in cuboid There would be six different surface areas So this is the front one exactly opposite to it. This would be the back one Then this side ones three four and top here and bottom here so six So these are six surface areas and these six surface areas guys. It is very Problematic if you don't it's it's one hour class for the timing has been written in the WhatsApp what's have grown so that the name of the class itself is centimars So we'll be here from eight to nine So if you look at it The complete space inside it is known as volume and Then we have surfaces so different surfaces front back Two sides right and left and then top and bottom in case of cuboid here. So We will be discussing about Different surface areas and and and volume Guys one more thing when centimars classes are going don't join at your behest because the timing is less. So join at Proper timing so that these kind of difficulties don't come so that I I I time and again have to do In I mean Get people in like see admit people time and again I don't know what do you mean by internet audio if you are Try to watch it from your Laptop you will not find these difficulties. So Okay Let me go to a cuboid the figure has already been made in front of you so This is the length this particular thing is length This is length. This is where so hg here is length and Gf here is width and Gb here is high And you look at here from edge to see if I draw this line at see here is diagonal fine, so What would be the volume? Volume is length into width and to height LBH. What is the diagonal? So diagonal is nothing but you look at here to draw the diagonal to find out the diagonal at see I draw fast hf So at see square is equal to hf square Plus FC whole whole square now Hf square is from this hf square is equal to Hg whole square Plus gf whole square. So I write here at see whole square is a g square Plus gf square plus FC square. So this is equivalent to Hg whole square is length square gf whole square is width square and fc whole square is Also parallel to Gb. So that is equal to Writing here FC is equal to Gb. So this is equal to h square. So diagonal is equal to under root L square plus V square So you have volume as LBH you have diagonal as L square plus B square plus h square Now generally there is a question asked in the examination that what would be the length of the longest rod that can be inserted diagonal always remember that either Inserted in the cuboid always remember whether it is cube or cuboid the longest possible side is the diagonal of that Cube or cuboid. So if somebody is asking you that what can be the Longest rod that can be inserted in a cube or cuboid it would be Nothing else but Please put your Microphones on silent so else it would be the length of the diagonal which is L square plus B square plus h square now Can you please put your microphones on silent? Okay. Now, let me go to The total surface area thing the total surface area thing would be here. So try to understand if you look at length and width this Upward and downward the area of The top floor and sorry the top top most the top and the bottom areas would be length into width and There are two surfaces to Similarly, the side ones would be B into H and there are a right one and left one so to be H plus Please put put your Microphones on silent Who is not once again? Then we have the Front front face and the back face. So that could be H H into L So total surface area would be equal to to LB plus BH plus HL Is it okay? Keep on writing this now. What is the perimeter of cuboid? Perimeter of cuboid you see here. We have length here. We have length here. We have length here We have length so four lengths. We have similarly one two three four four bits. We have and And we have one two three four four heights for four edge for L plus B plus H Is it okay? now What is the lateral surface area or lateral faces? So generally you are asked Lateral faces up you should understand lateral faces because you should you will have to find out lateral surface area Now lateral surface area is area of all the faces Which are meeting the bottom surface. So this is my top surface and this is my bottom surface So obviously top surface is not meeting the bottom surface Bottom surface is also not considered to be lateral surface. The surfaces which are meeting the bottom surfaces Are known as lateral surfaces. So this front face then this top Front face then this back face then right face and this left face. So four faces here would be Lateral surfaces. What is the lateral surface area? Keep on writing this lateral surface area would be nothing, but We have area of L into H. So two L Into H plus We have area of B into H. So two B into H. So you will have to look at look at the figure how it has been made This formula is not constant if I make the figure like this And I assume this to be L and this to be B and This to be H then you will have to change this formula. So don't mug up these formulas If nothing has been given then you have to assume like this. So two H L plus B is the area of lateral surface. Are you understanding it? Yes or no? So this is the area of lateral surface now. I'm moving to I hope you have written everything keep on writing things with me Now let me move to All these things have been given now cube is a special type of cuboid. There is no change in Cube format of the cuboid becomes cube when L is equal to B is equal to H when all length width and height are of same length So it becomes cube now you should know that let me go to some of the length of the edges It is 4L plus 4B plus 4H. Look at here now L plus B plus H, L, B, H are A So this becomes 3A So 4 into 3A is equal to 12A. Now under root diagonal is L square plus B square plus H square for cuboid So if all of them are A this becomes 3A square so A root 3 then Total surface area would be 2LB plus BH plus HL if all of them are same Then A square plus A square plus A square which is 3A square into 2 So 2A square 2 lateral surface area is 2HL plus B. So 2A A plus A so 2A into 2A is 4A square So you see here you get 4A square and volume is L into B into H So it becomes A into A into A which is equal to A cube. So it's something like this Now let me move to the other one, which is cross-sectional area So a cross-sectional area is defined like this So if I make a cut in solid perpendicular to its length, so if length is cut into different pieces And one more thing, so let me write here So if I make a cut through its length, and also And also, and also I'm getting distracted a lot with the chat messages and people joining late Cut through its length and also it should have same shape So then the cross-sectional area would be Sorry, volume of cross-section would be Area of cross-section multiplied by length And lateral surface would be perimeter of the cross-section multiplied by length Okay, so what am I discussing here? That is very important. So if I have, suppose a cylinder, let me teach you a cylinder now Suppose I have a cylinder, something like this Now what is the cross-sectional area? Look at the bottom area. This is the circular area. Is it okay? So across this cylinder, or let me make a horizontal cylinder like this Across the cylinder anywhere you go, you find cross-sectional area Equivalent to this circular area at top and bottom So that is what we are discussing that Volume till any point, volume of cylinder is Is equal to area of the cross-section So if radius of this circle is r, area of the cross-section would be how much? It's a circle, so pi r square multiplied by length. What is the length here? Suppose this length is l or h, whatever you assume. So if the length is l or h Then I can write it pi r square h. You look at here if this is r And this is h. So I can write this volume of cylinder as pi r square h. Now, what would be Lateral surface area? What is lateral surface area? Area which touches the bottom. So all this area except the area here Except the area at this bottom Everything here, the surface area This outer surface area is known as lateral surface And lateral surface would be perimeter of the cross-section. Perimeter of the cross-section is 2 pi r Multiplied by length. What is the length? Edge. So 2 pi r h Now in these kind of figures, in these kind of figures We also have something called total surface area So total surface area is Lateral surface area Plus area of Top and bottom So which is Area of lateral surface here is 2 pi r h And what is area of top and bottom? Bottom is pi r square here And top is what? Pi r square. So it is pi r square plus pi r square. How much it is? 2 pi r square So for a cylinder the volume is Pi r square h Area of lateral surface area is 2 pi r h And total surface area is equal to 2 pi r h plus 2 pi r square So if I take 2 pi r common I have r plus h So you need to remember this Is it okay? Yes or no? fine, so I have done till cylinder now. Let me go to uh cone and To do cone I'm doing cone here. So cone looks something like this So cone can be like this or cone can be something like this try to understand something like this So what is the difference between this first cone and this second cone? So this first cone if you look at the cross sectional area at the bottom The cross sectional area at the bottom is this circle. So this is suppose The radius is r here and this height is h here Now if you look at the length height here, it is making 90 degree angle if you drop Perpendicular from the vertex to the cross section. It is making 90 degree angle with the cross section That is why it is called a right Circular cone Is it okay? And it is Excuse me sir, your voice is breaking a lot Is my voice breaking? Hello No, sir Okay, fine Right circular cone now this kind of cone I'll discuss later though. It is not in uh Guys those who are having problem with voice or or sound quality log in again because For most of them it is going fine. So if if there is any problem you can Log out and log in again. That's absolutely not a problem. So this is right circular cone Now in right circular cone. What is the uh area area is Pyre square now Volume is one by three pyre square edge Then we have lateral surface area In this we defined slanted length l And slanted length in right circular cone would be l square is equal to h square plus r square In in this half triangle, which is a right angle triangle So lateral surface area is given by pi r l And total surface area would be Because there is no top here or or no bottom depending on how you keep your cone So total surface area would be pi r l Plus area of this circle, which is pi r square Is it okay? Yes or no So now we'll solve a few questions And uh There is a question flossing on your uh screen solve this question example one solve example one Okay, I'll write stairs. I'll write I teach you once again. I'll write when I revise at the end. I'll write Okay, enough time for this question the length width and Length width and height are in ratio. So l is to b is to h is is Six is to five is to four So you can directly write l is equal to six k b is equal to five k And c is sorry h is equal to four k What is the total surface area? Yes six l b b h and h l Six times six into five 30 k square b h 20 k square plus four into six is 24 k square is equal to five three two eight Now is it divisible by this divisible by Two because eight is coming 10 and plus 18 which is divisible by three also. So it is divisible by six So 50 plus uh, 24 is 74 k square is equal to five three two eight divided by six It gives me eight and then five two again. It gives me eight and again it gives me uh 48 so eight 88 comes out here And k square is equal to Uh, just give me a moment eight 88 divided by 74 Now what is the value of k square? Sir isn't total surface area equal to two l b plus b h plus h Sorry So this gives me 2664 And this comes out to be k square is equal to 2664 divided by 74 So if you do 2664 divided by 74 It gives you 36 k comes out to be six if k is six there is 36 There's 30 and this is 24 Right now let me go to another question Solve question number two Okay, enough time for this question. I'll not give you more than two minutes for any question So solve questions quickly now and Open rectangular system Is made of iron 2.5 centimeter thick Length is 125 Width is 105 centimeter And height is 90 centimeter now try to understand what is happening here If this is the bottom of or or This is how the system is What is happening out here is There is some thickness along the length along the width And height at the bottom not at the top because it's an open system So this width is 2.5 centimeter you understand like this that you have something like this And then there is 2.5 centimeter from everywhere So 2.5 from here and 2.5 from here And 2.5 from here and similarly 2.5 from here So it means that from everywhere length minus 5 Width minus 5 And height minus 2.5 why 2.5 because at the top surface We don't have any any covering surface over there. It's an open surface. So 2.5 would be lesser over there So Capacity internal volume would be removing this so 125 minus 5 is 120 105 minus 5 is 100 And 90 minus 2.5 is 87.5. So this is the internal volume In centimeter cube now one Sorry one meter cube is equal to thousand liters One centimeter cube is equal to 10 to the power minus three liters Because it becomes 10 to the power six centimeter cube is equal to thousand liters So one centimeter cube comes out to be 10 to the power three divided by 10 to the power six liters So 10 to the power minus three liters. So this is the area Now volume of the iron used how much volume has been used so total volume i'll find out and because the inside Inside volume is empty. It's a system. So it will be empty inside So total volume minus internal volume would be equal to volume of the iron used is it okay So total volume comes out here as 125 into 105 into 90 minus volume inside Where I I would be keeping something. So it would be 120 into 100 into 87.5 So how much it comes This comes out to be as it has been written here 131250 Now what's the total area try to understand What has been asked Total surface area of the system Okay, now The total surface area of the system would be try to understand if you have something like this And then you have something like this So total surface area would be Outer area plus this inside area. So area of the four surfaces plus area of the base So area of the four surfaces would be try to understand no top because there is nothing at the top. It's open So area of the base is equal to You look at here Area of the base is equal to length into width 125 into 105 this bigger area Area of the four surfaces here is This is lateral surface so two into 125 plus 105 Into 90 this is the area of external this external area total This would come out to be five four five two five Then internal area would be again area of the base so Area of the base is 120 into 100 plus lateral surface two into 120 plus 100 Into 87.5. This is the internal area Now area at the top there would be something area of the top. This is this is Not this is empty. So I can't add this area but here at the corners. There is Something left out. So area at the top would be equal to Area between the outer surface and inner surface. So outer surface is 125 this complete is 125 and from here to here it is 120. So 125 into 100 minus 120 into 105 and minus 120 into 100 So that gives me an area of 115 if I add all these areas. This is Five zero five double zero. So if I add five four this this and this this will be one zero six one five zero So that's your answer Somebody has made made this this mark Please remove it. It's not looking good This red line which is there at the screen This is not looking good Now let's try to solve some questions of cylinder so I've given you all the formulas of cylinder Okay Before I teach you Before I give you questions to solve cylinders Let me teach you this hollow right circular cylinder Hollow right circular cylinder you can see here Second cylinder is inside this first cylinder And inside this is hollow. So This is the first one This is hollow. There is nothing inside it And there is another cylinder like this, which is tapping it Something like this So inside it is nothing. So if somebody is asking you the thickness of the cylinder Thickness of the cylinder is this a smaller radius and this is the bigger radius So it is r minus r Area of cross section area of cross section is only this this much because Inside here. There is nothing so pi r square minus pi small r square. So area Now curved or lateral surface area is External curved surface area Plus internal curved surface area. So external curved surface area is 2 pi r h An internal would be 2 pi small r h. So you take 2 pi h common you have capital r plus a small r Now total surface area is This area plus this area. So pi r square minus pi r square Now volume of the material used volume of the material used is The lateral surface area Multiplied by height. So pi r square minus pi small small r square into h and volume of the hollow region is pi small r square into h So that's that that's that's what you have to do. So all the formula has been written on the board Uh, you can just copy it down in the next two to three minutes And in the next one minute, sorry and and solve the questions written on the example six Okay, solve example six now Okay enough time for this question So this question tells me that 2.2 cubic meter Cubic daisy meter of brass is Drawn into cylindrical wire of diameter 0.5 meter find the length of the wire So this question is very easy. First of all We need to convert one daisy meter is equal to 10 centimeter So one daisy meter cube would be equal to 10 into 10 10 to the power three centimeter cube Which is 1000 centimeter cube. So 2.2 cubic dm would be equal to 2200 centimeter cube Now cylindrical wire so cylindrical wire of diameter 0.25 centimeter It means that radius is point a point a diameter 0.5. So radius is 0.25 And is this centimeter? Yes, this is centimeter. So pi r square edge Is equal to volume volume is 2200 centimeter cube r has been given 22 by 7 into 0.25 into 0.25 is equal to 2200 So into h So this gives me thousand Okay 0.25 0.25 I write as one by four one by four. So these two fours go here So it gives me h is equal to thousand Into four into four and the seven also goes here So this gives me 16,000 into seven. No, isn't that 100? Where? Uh, 2200 divided by 22 is 100 It's 2200 right. I took it. I understood as thousand. Okay. No, it's So 100 so this gives me 1600 into seven Which is 112 double zero. So 112 double zero centimeter divided by 100 Edge comes out to be what 112 meters. Is it okay? Now solve question number seven So a well 14 meter diameter is dug eight meter deep So you have been given well is Generally like this cylindrical in nature So 14 meter diameter it means that radius is seven meter Eight meter deep H is eight The earth taken out of it has been evenly spread all around it To a width of 21 meter to form an embankment Find the height of the embankment so The earth which has been taken out is actually Lying out outside it Something like this All around it so What is it? This is seven. So what is the total volume total volume is pi small r square edge 22 by seven seven into seven into eight This and this one it gives me an answer of one two three two meter cube Find the area of the embankment area of this embankment This is the embankment. So it would be Pi capitals r square which has been given as 21 meter and Multiplied by subtracted by small r square so pi 28 square minus seven square so This gives me This is you Listen this width is 21. So radius would be how much 21 plus 7 28 that is why i'm writing 28 So pi into a square minus b square a plus b 28 plus 7 35 And 28 minus 7 is 21. So 22 by 7 into 35 into 21 This gives me 110 into 21 that will come out to be two three one zero meter square Now what would be the height of the embankment height of the embankment embankment would be volume of the Earth volume of the earth is one two three two divided by Area of the embankment area of the embankment is two three one zero multiplied by Let me find out and then i'll multiply because this will come out in meter meter cube divided by meter square Is meter And why it is multiplying here with 100 because it is converting it into centimeter So one three two three divided by two three one zero would be point three three three Meter if I convert it into centimeter. I multiply it with 100 it gives me 53.3 centimeter So I hope you understand it. Okay one more question The difference between outside and inside surface of cylinder example eight done One more minute. No Sharon wait, I don't think so vanisha Okay, let me solve this question The question tells that the difference between the outside and the inside surface of a cylindrical metal pipe 47 14 centimeter long is 44 centimeter square If the pipe is made of 97 cubic centimeter of metal Find the inner and outer radius of the pipe now try to understand the outer surface see The height is or the length is 14 centimeter So outer surface area would be 2 pi capital r h. So this gives me two into 22 by 7 into r into 14 So which comes out to be 44 into 288 capital r And internal surface area would be 2 pi small r h Is equal to 2 into 22 by 7 into small r into h So h is 14. So this gives me 88 small r So now subtraction difference between this area is 44 centimeter square So 88 capital r minus 88 small r Is equal to 44 So r minus r is equal to 44 by 88 That is equal to 1 by 2 Now Look at here the volume used for pipe would be equal to the lateral surface area Which is pi r square minus pi r square And whole multiplied by H So this gives me 22 by 7 r square minus r square into 14 And this is how much? 44 r square minus r square is equal to how much? 99 So R square minus r square is 99 by 44 Which is 9 by 4 So I can write it as r plus r Multiplied by r minus r is equal to 9 by 4. I know that r minus r is 1 by 2 So r plus r into 1 by 2 is equal to 9 by 4 So r plus r gives me 9 by 2 Now if I add these two equations 2 r comes out to be 9 by 2 plus 1 by 2. So 10 by 2 is 5 So capital r comes out to be 2.5 If capital r is 2.5 So 2.5 minus 0.5 small r will be equal to 2. That's the answer So This is the answer For today and this is the class for today. We have not done questions best on Cone and sphere and Hemisphere so that we will continue some other day And then we will Finish this off. So thank you so much for joining And We shall be meeting again for this topic So the class was Give me a moment Okay, so Thank you so much for joining. See you again. Fine. Thank you. Bye. Bye