If the radius of a cylinder doubled, keeping its lateral surface area

1.	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» 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%. C) Decreased by 50% Answer d decrease by 100%

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»

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%.

C) Decreased by 50%

Answer d decrease by 100%