Question

The total surface area of a cone whose radius is $\frac{r}{2}$ and slant height 2l is
(a) $2\pi r(l+r)$
(b) $\pi r\left(\mathrm{l}+\frac{\mathrm{r}}{4}\right)$
(c)$\mathrm{\pi r}(\mathrm{l}+\mathrm{r})$
(d) $2\pi rl$

Answer 1

(b) $\pi r\left(\mathrm{l}+\frac{\mathrm{r}}{4}\right)$

$$\begin{gathered} \mathrm{Total}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{cone}=\mathrm{\pi }\left(\frac{r}{2}\right)\times 2l\mathit{}+\mathrm{\pi }{\left(\frac{r}{2}\right)}^2 \\ =\mathrm{\pi }\left(rl+\frac{r^{\mathit{2}}}{4}\right) \\ =\mathrm{\pi }r\left(l+\frac{r}{4}\right) \end{gathered}$$