### 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.

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**Answer: **8:1

**Step by Step Explanation: **- We know that the volume of a cone with radius r and height h = πr
^{2}h. - We also know that the volume of a sphere with radius r = πr
^{3}. - We have been told that the volume of the sphere is half the volume of the cone.

Therefore, πr^{3} = × ( πr^{2}h)

or, = 8:1 - Thus, the ratio of the height and radius of the cone is
**8:1**.