Question

If the height of a cylinder becomes `1/4` of the original height and the radius is doubled, then which of the following will be true?

Options

• Volume of the cylinder will be doubled.

• Volume of the cylinder will remain unchanged.

• Volume of the cylinder will be halved.

• Volume of the cylinder will be `1/4` of the original volume.

Answer 1

Volume of the cylinder will remain unchanged.

Explanation:

We know that, the volume of a cylinder having base radius r and height h is V = πr²h

Now, If new height is `1/2`th of the original height and the radius is doubled, i.e. h’ = `1/4`h and r’ = 2r, then

New volume, V’ = `pi(2r)^2 xx 1/4 h`

= `4pir^2 xx 1/4h`

= `pi^2h` = V

Hence, the new volume of cylinder is same as the original volume.