Question

The radius and height of a cone are in the ratio $4:3.$ The area of the base is $154c{m}^2$. The area of the curved surface in $c{m}^2$ is ___

Answer 1

Given, $\frac{r}{h}=\frac{4}{3}$

Base area $=\pi r^2=154$

$\Rightarrow r=7cm,$ so, $h=\frac{3}{4}\times 7=\frac{21}{4}$
$\Rightarrow l=\sqrt{(h^2+r^2)}=\frac{35}{4}$

$\Rightarrow$ So, curved surface area $=\pi rl$

$\Rightarrow \frac{22}{7}\times 7\times \frac{35}{4}=192.5c{m}^2$