<u>Given</u>:
The volume of a cylinder is cubic units.
A cone shares the same base.
The height of the cone is twice the height of the cylinder.
We need to determine the volume of the cone.
<u>Height of the Cone:</u>
Let h denote the height of the cylinder.
Let H denote the height of the cone.
Since, it is given that, the height of the cone is twice the height of the cylinder, we have;
<u>Volume of the cylinder:</u>
The formula to determine the volume of the cylinder is
Since, volume of the cylinder is , we get;
-------(1)
<u>Volume of the cone:</u>
The formula to determine the volume of the cone is
Substituting , we get;
Substituting equation (1), we get;
Thus, the volume of the cone is 20π
Hence, Option C is the correct answer.