Question

If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Let the radius and height of a cylinder be r and h respectively.

Curved surface area of a cylinder = 2πrh

If the radius of a cylinder = 2r and height = H. 

And curved surface area of a cylinder is not changed.

∴ 2πrh = 2π(2r) × H

`\implies H = (2pirh)/(4pir)`

`\implies H = h/2`

Hence, the height of a cylinder must be halved.