Question

The area of the curved surface of a cone is $60\pi c{m}^2$. If the slant height of the cone is $8$cm, find the radius of the base.

Answer 1

We know that the curved surface area of a cone with radius $r$ and slant height $l$ is $CSA=\pi rl$.

It is given that the curved surface area of the cone is $CSA=60\pi$ cm${}^2$ andthe slant height is $l=8$ cm, therefore,

$CSA=\pi rl\Rightarrow 60\pi =\pi \times r\times 8\Rightarrow 60=8r\Rightarrow r=\frac{60}{8}=7.5$

Hence, radius the cone is $7.5$ cm.