Question

Curved Surface area of a cone is $308c{m}^2$ and its slant height is $14cm$. Find
(i) radius of the base
(ii) Total surface area of the cone.

Answer 1

Curved surface area of a cone of radius ${}^{\prime }{r}^{\prime }$ and height ${}^{\prime }{h}^{\prime }$ and slant height ${}^{\prime }{l}^{\prime }$ is given by $\pi rl$.

$i)$ Curved surface area$=308{cm}^2$

$l=14$cm

$\pi rl=308\Rightarrow \pi \times 14\times r=308\Rightarrow \frac{22}{7}\times 14\times r=308\Rightarrow 22\times 2\times r=308$

$\Rightarrow r=\frac{308}{44}7$cm

$ii)$ Total surface area$=$curved surface area $+$ area of the base

$=\pi rl+\pi r^2=\frac{22}{7}\times 7(14+7)=22\times 21=462{cm}^2$