# Question #75d5c

##### 1 Answer

#### Explanation:

A cone circumscribes a sphere and has its slant height equal to the diameter of its base. Show that the volume of the cone is 3/4 the volume of the sphere?

Given:

Slant height equal to diameter of the base.

ie,

the cone has 2 slant heights and one base which are all equal, and forming an equilateral angle

The angle at the vertex is 60 degrees

Semi vertex angle is

If the slant height is

radius of the circumscribed sphere is

Angle between the radii is

Thus

Now,

Volume of a sphere is V1

radius of the cone is

Height of the cone is given by

Volume of the cone is V2

Thus,

Volume of sphere is

Volume of the cone is