### A sphere and a cone have the same radius. If the volume of the sphere is half of the volume of the cone, find the ratio of the height and radius of the cone.

8:1

Step by Step Explanation:
1. We know that the volume of a cone with radius r and height h =
 1 3
πr2h.
2. We also know that the volume of a sphere with radius r =
 4 3
πr3.
3. We have been told that the volume of the sphere is half the volume of the cone.
Therefore,
 4 3
πr3 =
 1 2
× (
 1 3
πr2h)
or,
 h r
= 8:1
4. Thus, the ratio of the height and radius of the cone is 8:1.