Question

Curved suface area of a cone is $308c{m}^2$ and its slant height is $14cm$. Find the radius of the base and total surface area of the cone.

Answer 1

Given,
Curved surface area pf cone = $308c{m}^2$
Slant height of cone $\left(l\right)=14cm$

Let radius of cone be $r$
$\because$ curved surface area of cone $=\pi rl$
$\Rightarrow \pi rl=308$
$\Rightarrow \frac{22}{7}\times r\times l=308$
$\Rightarrow r=\frac{308\times 7}{22\times 14}=7$

Hence, radius of cone = 17 cm

$T.S.A.$ of cone $=\pi rl+\pi r^2$
$=\pi r(l+r)$
$=\frac{22}{7}\times 7\times (14+7)$
$=462$

Hence, total surface area of aone is $462c{m}^2$