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) $\pi r(l+\frac{r}{4})$
C) $\pi r(l+r)$
D) ​​​​​​​$2\pi rl$​​​​​​​

Answer 1

The answer is B: $\pi r(l+\frac{r}{4})$

Given, radius $=\frac{r}{2}$ and slant height $=2l$
$\therefore$ Total surface area of a cone $=$ Curved Surface Area $+$ Base Area

$=(\pi \times$ radius $\times$ slant height) $+\pi \times$ radius${}^2$

$=\pi \times \frac{r}{2}\times \left(2l\right)+\pi \times (\frac{r}{2}{)}^2$

$=\pi rl+\pi \frac{r^2}{4}$

$=\pi r(l+\frac{r}{4})$