Question

If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.

Answer 1

In the given problem, we are given a cone and a sphere which have equal volumes. The dimensions of the two are;

Radius of the cone (r_c) = r

Radius of the sphere (r_s) = 2r

Now, let the height of the cone = h

Here, Volume of the sphere = volume of the cone

`(4/3)pi r_s^3 = (1/3)pi r_c^2 h`

`(4/3)pi (2r)^3 = (1/3) pi (r)^2 h`

`(4/3) (8r^3)=(1/3)r^2 h`

Further, solving for h

 

`h = ((4)(8r^3))/((r^2))`

Therefore, the height of the cone is 32r.