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= (4)/(3) \pi r^(3)`. If we calculate it, we'll obtain
`V=288 \pi`