I students, welcome to the section where we deal with solids, now we start with identifying the volume
of a cuboid.
All right.
Now, before we get to a cuboid, let's think of what we mean about volume.
Volume is the amount of space occupied by a three dimensional object.
All right.
Now, over here we have a cube, right?
So over here, the length, breadth and height all is equal to one centimeter.
And this space, this amount of space is what we define as one centimetre cube.
That is one centimeter into one centimeter into one centimeter.
All right.
Now, over here, I have a cuboid right now.
You can see that in this cuboid, eight cubes are included.
Right.
So you have included aid groups.
That is one, two, three, four, five, six, seven, eight.
Therefore, the volume of this cube out over here has to be eight times the volume of this cube.
Right.
So that is equal to eight to one, which gives you eight centimetre cube.
All right, now, let's keep this aside.
Let's try to find out how we can find the volume of any cuboid now over here, because we kept four
cubes side by side, the length has become four centimeter, the bread is just one centimeter.
And you can see that the height over here is one plus one.
That's two centimeters right now.
You can see that the volume, which is what we got over here, can be found by multiplying four, two
and one.
So volume is four in the two in the one that's equal to eight centimeters.
And that's the same value that we got over here.
Now you can see that over here to find the volume.
What we have done is we have found the area of the base that's four into one and then multiply it with
the height.
So volume is equal to area of the base into height.
Now, this can be used for any shape where the base and the top, where the bottom and the top are congruent.
Right.
For example, will see that the same is applicable in the case of a cylinder.
Also over here, in the case of a cylinder, you can see that the bottom and the top are congruent and
it has a height.
So over here also, you can apply this formula that is the volume would be area of the base into the
height.
Now let's proceed with Cuboid and quickly revise what we have learned and also learn some more interesting
properties.
But over here we have a cuboid of Langdell, Brett B and Height Edge.
Now, over here you can see this shape has six faces, twelve edges and eight.
What is this now?
What are the faces?
For example, this is one face similar to this over here is one face and this is the third face.
Now you can see that there are three more faces, right?
You have one over here, one at the bottom and one behind this one.
But there are a total of six faces now.
It just are these sites.
OK, so there is one, two, three, four.
That's Force A just.
And then on the back side, also, you will have four, the four plus four and over here you have one
and this is another one that's two.
And similarly over here also you have one and over here you can have one more.
So that's four plus four plus two plus two.
That's equal to twelve edges.
And what about what it says?
It has eight vertices.
So what is this are the corners.
So that's one, two, three and four.
And you'll have four on this side also.
That's four plus four.
It's equal to eight.
What is this?
All right.
What about the lateral surface area of the keyboard and what is the lateral surface area?
It's the area that let me clean this up and show you what we mean with the natural surface area.
It's this area or here, this one plus this one plus the side opposite to this and the side opposite
to this.
Right.
So the little surface area is equal to two times this area.
Let's do the last two times this area.
So that is equal to two times into it for this one and two times B Interreg for this one little area
is equal to two times Elitch plus two times, be it.
Now what about the total surface area?
To find the total surface area, you need to add the top area and the bottom area to the lateral surface
area.
So the total surface area is equal to two times L, B plus B plus L, right.
l.B gives you the bottom and top.
Right, two times B, which is this and this side.
And then you have Elitch, which is this side and the one in the other side of it.
Now that's the total surface area.
We call it DRC.
Now what about the volume?
We have seen that the volume is in the bread into height.
Right.
And the last property that we learn over here is that the length of the body diagonal is root of L squared,
plus B squared, plus eight square.
Now, what is a body diagonal?
Let me clean this up a bit.
The body diagonal would be the line segment joining this point over here with this point over here.
So it is the largest line segment that you can put inside that quote.
And that would be root of L squared, plus B squared, plus eight square right now.
Why is that?
So let's dig in lower here and be over here.
Now, this diagonal would be root of L squared plus B squared.
Right, ASPO Pythagoras's theorem.
Now let's add it to it.
It is also perpendicular if you take this one, this is the body diagonal that would be a square root
of it.
Squared plus square off root and squared plus B square.
Right when you square root of L Square please B square you will get just L squared plus B square and
you have it square also over here.
Therefore the length of the body diagonal of a cuboid will be root of L squared plus B squared plus
it's square.