Question

If the height of a cylinder becomes$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ the original height and the radius is doubled, then which of the following will be true?

• A. The curved surface area of the cylinder will be doubled.
• B. The curved surface area of the cylinder will remain unchanged
• C. The curved surface area of the cylinder will be halved.
• D. The curved surface area will be $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ of the original curved surface.

Answer 1

The correct option is C

The curved surface area of the cylinder will be halved.

The explanation for the correct option.

Find the change in the curved surface area of the cylinder.

Let the height of the cylinder is $\mathrm{h}$and the radius of the cylinder is $\mathrm{r}$.

The curved surface area of the cylinder $=2\mathrm{\pi rh}$.

If the height becomes $\frac{\mathrm{h}}{4}$and radius becomes $2\mathrm{r}$.

The curved surface area of the cylinder after changing the height and radius $=2\mathrm{\pi }\left(\frac{\mathrm{h}}{4}\right)\left(2\mathrm{r}\right)=\mathrm{\pi hr}$.

$$\begin{gathered} \frac{\mathrm{CSA}\mathrm{after}\mathrm{changing}\mathrm{dimension}}{\mathrm{CSA}}=\frac{\mathrm{\pi rh}}{2\mathrm{\pi rh}} \\ =\frac{1}{2} \end{gathered}$$

C.S.A. after changing dimension $=\frac{1}{2}$ original C.S.A.

Therefore curved surface area becomes halved of the original CSA.