Question

State True or False:

If the radius of a cylinder is doubled, the height of the cylinder should be halved in order to keep the curved surface area unchanged.

• A. True
• B. False

Answer 1

The correct option is A True

Let, the original radius be $r$ cm and original height be $h$ cm

Formula for Curved Surface Area of the cylinder$=2\pi rh$

For new cylinder,

New Radius $r_1=2r$ cm

Let, New height be $h_1$ cm

Now, according to question

$2\pi rh=2\pi r_1{h}_1$

$\Rightarrow rh=2r{h}_1$

$\Rightarrow h_1=\frac{h}{2}$

This proves that height must be halved to have the same curved surface area when radius is doubled.