Let's do this question, a rectangular sheet of dimensions, twenty five centimeters into seven centimeters
is rotated about its longer side.
Find the volume and the whole surface area of the solid that's generated.
All right.
What's the video?
Give it a try and then let's do it together.
All right.
We're back.
Let's do it together.
Now, if you take a rectangular sheet of paper, right, and you rotated about, it's longer same.
So let this be the longer side.
But what does rotating it about the longest side mean, you keep turning it like this, right?
So this will turn out to become a cylinder.
Right, so you get a cylinder when you rotate a rectangular sheet, all right.
Now, what would be the dimensions of the cylinder?
The dimensions would be twenty five centimeters would be the height.
Right.
Because that's this height over here.
And we have rotated it about its longer side.
Right.
That's why you can see from the figure this will be twenty five centimeter and this part.
Right.
This is this was the initial sheet that we had.
And we know this is equal to seven centimeter and that is the radius of this base over here.
Right.
Therefore, the radius is seven centimeter and the height will be twenty five centimeters.
Now we need to find the volume and the whole surface area of the solid.
Right.
So volume is biased coverage for a cylinder that's equal to twenty two by seven inch to seven square
inch to twenty five.
And this simplifies two three eight five zero centimetre cube.
All right.
Now what about the surface area.
That's two Pyar Square because you have two bases plus two Pyaar.
It's right to surface area.
Total surface area is to Pyaar squared plus two by our edge.
Let's substitute values.
That's two hundred twenty two by seven to seven squared plus two in twenty two by seven into seven into
twenty five.
And that simplifies two one four zero eight centimeter square.
That is your answer.