Students in this video, let's discuss about the right circular cylinder.
All right, now let's take an example.
Over here, you have a right circular cylinder.
Now, why is it called the right circular cylinder?
You could have a cylinder like this also, right?
Right over here, this axis is not perpendicular to this axis, right, but here you can see this is
perpendicular to the base.
So this type of a cylinder is what we call a right circular cylinder.
And we only deal with this in this course.
And even for your exam, you just need to learn about the right circular cylinder.
All right.
Now let's start to understand the surface area of the cylinder.
Now, over here, imagine I'm cutting out this cylinder and opening it up like this.
Now, let the height of the cylinder, be it and the radius of this part.
Right.
The circular part we are now, you can see that in this case, this will be X and this will be equal
due to the right way to appear, because this is the circumference.
Of this base, that's what we cut and spread out, right, therefore, this length will be to pay up
and this will be it.
Now we know how to find the area over here that would be too far into its right because this looks like
a rectangle now.
And we know area of a rectangle this length and breadth.
Therefore, this area over here is to peer into it.
All right.
Now, what would be the area of this circular path?
That would be Pyaar Square, right.
We know that's the area of a circle.
Now, having established this, let's note the lateral surface area of this.
Right.
Circular cylinder that would be to by our edge, which is what we got over here to the NSA of a right
circular cylinder is to buy up its what about the TSA or total surface area that would be to Biarritz
plus to Pyaar Square.
Right.
Why is that so?
Because you have a circular area at the bottom and at the top, that's why you need to multiply by square
with two and you add to that the lateral area.
So this is the total surface area.
All right.
So we have learned how to find the natural surface area and the total surface area of a right circular
cylinder.
Let's move on now.
Over here.
We have our cylinder and this is radius R and this is height.
It's now like a cuboid.
You can see that the cylinder has a top and a base that are congruent and parallel to each other.
Right.
This double here and this base.
Both are Sakalys.
They are congruent and they are parallel to each other.
Therefore, we can find the volume of this cylinder in the same way we found the volume of the cuboid
that is volume is equal to the base of the area of the base.
In the height of any of the base is Bayada Square.
So volume over here is Spier Square into X, and that is the way you can find the volume of a cylinder.
So we have seen how to find the large area, total surface area and volume of a cylinder.
Now let's take a special case that is the case of a hollow cylinder.
Now what is a hollow cylinder?
It looks like this.
Now, this is a rough sketch of a hollow cylinder.
You can see that there is a space inside it which is hollow right over here.
It's completely filled.
But over here, you can see there is one more circle over here and anything inside this is hollow.
So this is an example of a hollow cylinder.
Imagine a pipe which is very thick.
Right.
So water can flow through it.
So there is some hollow space inside.
But imagine that it's very thick.
So that would be an example of a hollow cylinder.
Now, how do we find the volume of a hollow cylinder that would be piled into our square minus our square
into its where capital R is this radius over here and smaller is this radius over here.
Now, what is the logic behind this?
This is the same as by our square inch, which is what we had over here, minus by our square inch.
Right.
So that's logical because this is the volume.
If it was not hollow and we are just subtracting the part where it's hollow.
So that is the volume that's to our square minus our square into a.