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 is __ $c{m}^2$

Answer 1

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

Base area $=\pi r^2=154c{m}^2$

$\Rightarrow r^2=\frac{154\times 7}{22}=49$

$\Rightarrow r=7cm$ 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 $=\pi rl$

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