Question

Curved surface area of a cone with base radius 40 cm is 1640 $\mathrm{\pi }$ sq.cm. Find the height of the cone.

Answer 1

Given:
Curved surface area of the cone = 1640$\mathrm{\pi }$ cm²
Base radius (r) = 40 cm
We know:
Curved surface area of the cone = $\mathrm{\pi }$rl
$\Rightarrow$$\mathrm{\pi }$rl = 1640$\mathrm{\pi }$
$\Rightarrow$40$\mathrm{\pi }$× l = 1640
$\Rightarrow$l = 41 cm
Also,
Slant height, l = $\sqrt{r^2+h^2}$
$$\begin{gathered} \Rightarrow h=\sqrt{l^2-r^2} \\ =\sqrt{{41}^2-{40}^2} \\ =\sqrt{81} \\ =9\mathrm{cm} \end{gathered}$$

Hence, the height of the cone is 9 cm.