Question

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

Answer 1

Given, radius $r=40cm$ and curved surface area of the cone $=1640\pi c{m}^2$.

We know, the curved surface area of a cone $=\pi rl$.

Hence, curved surface area of this cone $=\pi \times 40\times l$

$\Rightarrow \pi \times 40\times l=1640\pi$

$\Rightarrow l=41cm$

Now, for a cone, slant height $l=\sqrt{h^2+r^2}$

Hence, $41=\sqrt{h^2+{40}^2}$

$\Rightarrow 1681=h^2+1600$

$\Rightarrow h^2=81$

$\Rightarrow h=9cm$.