Question

In a cylinder, radius is doubled and height is halved, curved surface area will be

• A. halved
• B. doubled
• C. same
• D. four times

Answer 1

The correct option is C

same

Explanation for the correct option:

Find the new curved surface area:

• Let the original radius be $r$ and the original height be $h$
• Then the new radius will be $2r$ and the new height will be $\frac{h}{2}$

Curved surface area of a cylinder is$=2\mathrm{\pi }\left(\mathrm{R}\right)\mathrm{H}$

Original curved surface area$=2\mathrm{\pi rh}$

New curved surface area$=2\mathrm{\pi }\left(\mathrm{R}\right)\mathrm{H}$

$$\begin{gathered} =2\mathrm{\pi }\times \left(2\mathrm{r}\right)\times \left(\frac{\mathrm{h}}{2}\right) \\ =2\mathrm{\pi rh} \end{gathered}$$

Hence, the correct option is $\mathbf{option}\mathbf{}\left(C\right)$.