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

• Curved surface area of the cylinder will be doubled.

• Curved surface area of the cylinder will remain unchanged.

• Curved surface area of the cylinder will be halved.

• Curved surface area will be `1/4` of the original curved surface.

Answer 1

Curved surface area of the cylinder will be halved.

Explanation:

Let the new height and radius be `h/4` and 2r respectively, where r and h are original radius and original height respectively of the cylinder.

We know that, curved surface area of cylinder = 2πh

Then, curved surface of the new cylinder

= `2pi(2r) xx 1/4h`

= `4pir xx 1/4h`

= πrh

= `1/2 xx 2pirh`  ...[Multiplying and dividing by 2]

= `1/2` original curved surface area

Hence, the curved surface area of the cylinder will be halved.