Question

If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be

• A. tripled
• B. constant
• C. one sixth
• D. one third

Answer 1

The correct option is D

one third

Explanation for the correct option.

Let the height of the cylinder is $h$and radius is $r$.

We know that curved surface area of the cylinder is given by:

$A=2\mathrm{\pi rh}$

Let changed height is $h\text{'}$.

Given: The radius of a cylinder is tripled but its curved surface area is unchanged.

Therefore,

$$\begin{gathered} 2\mathrm{\pi }\left(3\mathrm{r}\right)\mathrm{h}\text{'}=2\mathrm{\pi rh} \\ \Rightarrow \mathrm{h}\text{'}=\frac{1}{3}\mathrm{h} \end{gathered}$$

Hence, the changed height is one-third of the previous height.

Option $D$ is the correct answer.