Question

A cone has a slant height of 10 centimeters and a lateral area of 60π square centimeters. what is the volume of a sphere with a radius equal to that of the cone?

Answer 1

The surface area of a cone is $A= \pi r^{2}+ \pi r \sqrt{ h^{2} + r^{2} }$. Lateral area is $A= \pi r \sqrt{ r^{2} + h^{2} }$. Here $\sqrt{ h^{2} + r^{2} }$ is a slant height. 

Using this information we can write that $60 \pi =10 \pi r$ and r=6 cm

The volume of the sphere is given by $V= \frac{4}{3} \pi r^{3}$. If we calculate it, we'll obtain $V=288 \pi$