Question

The total surface area of a right circular cone of slant height $20cm$ is $384\pi c{m}^2$.
Calculate: (i) its radius in $cm$;
(ii) its volume in $c{m}^3$, in terms of $\pi$.

Answer 1

T.S.A. $=\pi r^2+\pi rl=384\pi {\text{cm}}^2$

$⟹\pi (r^2+r\times 20)=384\pi$

$⟹r^2+20r-384=0$

$⟹r=12,-32$

Considering the value $r=12\text{cm}$ as radius cannot be negative.

Volume $=\frac{\pi }{3}{r}^{2}h$

$=\frac{\pi }{3}\times {12}^2\times 16$

$=2412.7{\text{cm}}^3$