Introduction of mensuration/Surface area of cuboid and cube

追加: 2026-06-03

[00:00:05]Welcome. Today we are going to learn about the introduction class of maturation of class 9 maths which is included in chapter 13.

[00:00:16]As you all are the students of the class 9. I believe you have already uh known about these figures. This is circle.

[00:00:25]This is square and this is rectangle.

[00:00:29]And as I'm trying to give you the uh more revision which we have already uh learned in the previous classes you know the area of the circle is pi r² and the perimeter that is the circumerence of this circle 2 pi r and the area of this square is uh l² and the perimeter which is the boundary of The square is 4 L and the area of the rectangle is length into bread. This is the length of the rectangle and this is the breadth of the rectangle. So the area of the rectangle is given by length into breadth. And the perimeter of the rectangle which is the sum of all these uh length of this rectangle is two whole in two bracket length plus bread 2 L + B.

[00:01:35]Now again we will see about solid figures. Uh you all know that solid figures uh the examples the examples of solid figures are cuboid, cube, isphere and con. So in case of the cuboid uh there are the lots of examples of cuboid but uh you can take one example uh one uh very easy example you all have in your own home that is the maths box and in case of the cube uh you can see the you all uh know about the game lud ludoo I think that the dice of the ludu the that shape is a cube and in case of the isphere it is a solid bowl. Uh if uh you have a one football and the if the inside of the football is all solid then that is the example of the sphere. And uh in case of the con uh I think you all like ice cream very much as now it is summer also. The bottom part of the ice cream uh which can which hold the ice part ice cream part that is the cone.

[00:02:44]That is the example of the con and I will tell you about the cuboid. Uh these are the some rough uh diagram of the cuboid and it has the six faces but uh the face the it has the different leng bread height and in case of the cube it has the six faces but the face it is the square in so it has the length I mean by that is the leng bread height of a cube is all same but in case of the cuboid leng bread height are all different. Okay.

[00:03:24]So, okay. Uh now for the cuboid there are the two type of surface area. One is the total surface area and another is the lateral surface area.

[00:03:40]What do we mean by the total surface area and the lateral surface area? Let's see.

[00:03:48]uh in case of the cuboid it has the six face.

[00:03:53]If I want to find out the total surface area of all the faces of the cuboid that is called the total surface area of a cuboid. And the formula of the total surface area of a cuboid is 2 whole into L into B plus B into height plus 8 into L. That is 2 whole into length into bread plus bread into height plus height into length bracket close. And the formula of the lateral surface area of a cuboid is two whole into length plus bread bracket close into height.

[00:04:42]Okay, let's see how a cuboid is built of.

[00:04:48]This is the one side of a cuboid.

[00:04:52]And then now we have another side. And there is also another side. There is also now another side. And on top of it there is also another side. In total it has the six faces.

[00:05:14]If I cut this tuboid and uh want to make it into a plan paper, the plan uh plan figure the plan figure will come out like this.

[00:05:33]This is the bottom side and this another side will come out like this.

[00:05:40]And this side will come out like this.

[00:05:44]And this side will come out like this.

[00:05:48]And this side will come out like this.

[00:05:52]And the top face will come out like this.

[00:06:01]Now you see the blend figure of it. It has the length, breadth and height.

[00:06:10]So uh let's see. Let's demonstrate. Uh the mats box.

[00:06:16]This is the mats box.

[00:06:18]Okay. This is the mats box. And it has the six fest. 1 2 3 4 5 6. You see? You see? One 2 3 4 5 and six. It has a six face and let's see whether it come out like this or not. I will cut this matchbox and let's see.

[00:07:00]Okay, these are coming out like this.

[00:07:25]See, it's coming out like this.

[00:07:29]It's like this.

[00:07:32]I'll put here.

[00:07:38]This side is this one. And then one 2 3 4 5 6. These are the six faces.

[00:07:55]And this longest one is represented by the length here also. And then this uh the sort the middle one and then this is the shortest one. The shortest one is represented by the longest one length is represented by L.

[00:08:34]Here the length is represented by L. And then the bread is represented by B. And the height is represented by H. And we already learned that in case of rectangle this face is a rectangle. So you look at the uh face number one. It is a rectangle in Sep. So the area of this face one the area of this face one is this is L and this is B. So the area of this face one is L length into bread and then these two the area of this face two is this is L and this shortest one is H. So, LH and then the area of this face tree is when we close this figure like this is same to this one that is the okay now we'll find out how to find out the surface area this figure is similar to this figure and It has the one uh face number one, face number two, face number three, face number four, face number five and face number six. And if I want to find out the surface area, then I have to find out this surface area and this surface area, this surface area, this surface area and this surface area and this surface area and I have to sum up all the surface area.

[00:10:24]But in case of the total surface area what we have to do is we have to find out all the total surface area of this cuboid. But what is mean by the lateral surface area? Lateral surface area is any lateral surface area of a figure is the surface area of that figure without the to and the bottom of it without the this to the bottom of it. Okay. So it the lateral surface area of a cuboid will be the only the surface area of this site of this side of this side and of this side.

[00:11:14]So now we will find out the total surface area that is the sum of all the six faces the surface area of these six faces. For face number one, you will find out the area of this face number one. This face number one. This face number one.

[00:11:38]This is rectangle in safe. You see this?

[00:11:41]I will cover all the other. This is rectangle in safe. So face number one length into bread. Likewise for face number two that is only this part that is only this part. The area of this part is length into height.

[00:12:02]Likewise for face number three what it is? It is length and bread. So LB for face number four it is L and it's length into height. For face number five it is braid into height. For face number six it is braid into height. So in case of total surface area we have to sum up all of these face number 1 2 3 4 5 6. So the so total surface area of a cuboid we have to sum up all these face number one, face number two, face number three, face number four, face number five and face number six. That is length into bread plus length into height plus length into bread plus length into height plus bread into height plus bread into height. So we will see there are two lang into bread it will sum of and then two lb and then two leng into h there are two lh plus same there are two b into h we can take two common out 2 lb + l + b H.

[00:13:43]So in order to look more beautiful we can write like this also LB BH and H L. This is same LB is here and then BH is here and then LH we can write as H L. Now then this is the formula of the total surface area of a cuboid.

[00:14:16]If you know how the formula has been built up, you can easily memorize this formula also.

[00:14:23]Now lateral surface area lateral surface area of a cuboid.

[00:14:37]What did I say before? Lateral surface area. It is the surface area of that figure without the top and the bottom part. That is in this figure. The top and bottom is this one. And then the bottom one that is here. What is this figure here? Here.

[00:15:01]This one. And then the bottom part will be this one. This one and this one.

[00:15:08]Without these two faces the if we sum up the remaining part we will find out the lateral surface area.

[00:15:21]See let's see without this face number one and face number three. If we sum up face number two without this face number one and without this face number three that is let's see from the figure without this one and without this one if we sum up the remaining faces we will find the lateral surface area of a cuboid that is this face this face this face and then this face only. So we will see now we have to the top uh face is face number one and bottom is face number three. So we will add up only face number two face number four face number five and face number six. Lateral surface area of a cuboid is LH + LH + BH + BH.

[00:16:25]Therefore, there are two LH and then this one is 2 LH and then this one is 2 BH. to BH.

[00:16:37]So we can take there are H there's also another H. So we can take H common out and then L + B.

[00:16:50]So now we can write like this also L + Bids we will give here. These are the multiplication of two I 2 into whole into L + B.

[00:17:08]This is similar to this is one. This one. So the lateral surface area of a cuboid is 2 into L + B bracket close H.

[00:17:22]So like this you can find out the total surface area of a cube and lateral surface area of a cube. Uh by using this formula this formula and likewise the you can remember or you can buy her total surface area of cuboid and lateral surface area of cuboid which I taught before. So that's all for today. You will find uh the solutions of the exercise uh 13.1 uh in my next video.

[00:17:54]And let's wait for the next video.