Question

If the radius of a cylinder doubled, keeping its lateral surface area the same then its height is………………. 

A) Increased by 50% 

B) Increased by 100%

C) Decreased by 50% 

D) Decreased by 100%

Answer 1

Correct option is (C) Decreased by 50%

Let r and h be parameters of original cylinder & R and H be parameters of another cylinder.

Let R = 2r

Also \(2\pi RH=2\pi rh\)    (Given)

\(\Rightarrow\) \(H=\frac{2\pi rh}{2\pi R}=\frac{rh}{2r}=\frac h2\)   \((\because\) R = 2r)

\(\therefore\) Height is decreased by 50%.

Answer 2

C) Decreased by 50%

Answer 3

Answer d decrease by 100%