Question

A solid cylinder of radius $r$ and height $h$ is placed over another cylinder of the same height and radius. The total surface area of the shape so formed is:

• A. $4\mathrm{\pi rh}$
• B. $4\mathrm{\pi rh}+2{\mathrm{\pi r}}^2$
• C. $\mathrm{\pi rh}+{\mathrm{\pi r}}^2$
• D. none of these

Answer 1

The correct option is B

$4\mathrm{\pi rh}+2{\mathrm{\pi r}}^2$

Here height of cylinder $=2h$

Radius$=r$

TSA of cylinder $=2\mathrm{\pi r}(\mathrm{h}+\mathrm{r})$

$$\begin{gathered} =2\mathrm{\pi r}(2\mathrm{h}+\mathrm{r}) \\ =4\mathrm{\pi rh}+2{\mathrm{\pi r}}^2 \end{gathered}$$

Hence the correct option is $B$.