Question

The volume of a cone is the same as that of volume of a cylinder whose height is 9 cm and diameter 40 cm. Find the radius of the base of the cone if its height is 108 cm.

Answer 1

Let $r_1,h_1$ and $r_2,h_2$ be the radius and height of of cone and cylinder respectiely.

Given, $h_2=9cm,d_2=40cm$
$r_2=\frac{40}{2}=20cm,h_1=108cm$.
Volume of the cone $=$ Volume of the cylinder.
$\frac{1}{3}\pi r_1^2{h}_1=\pi r_2^2{h}_2$
$\frac{1}{3}\pi r_1^2\left(108\right)=\pi \left(20{)}^2\right(9)$
$r_1^2\left(108\right)=3\times 9\times (20{)}^2$
$r_1^2=\frac{3\times 9\times 400}{108}$
$r_1^2=100cm$.
$r_1=10cm$
Thus, the radius of the base of the cone is $10cm$.