<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;
![H=2h](https://tex.z-dn.net/?f=H%3D2h)
<u>Volume of the cylinder:</u>
The formula to determine the volume of the cylinder is
![V=\pi r^2 h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2%20h)
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
![V=\frac{1}{3} \pi r^2 H](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20H)
Substituting
, we get;
![V=\frac{1}{3} \pi r^2 (2h)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20%282h%29)
![V=\frac{2}{3} \pi r^2 h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E2%20h)
Substituting equation (1), we get;
![V=\frac{2}{3} (30 \pi)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%7D%7B3%7D%20%2830%20%5Cpi%29)
![V=20 \pi](https://tex.z-dn.net/?f=V%3D20%20%5Cpi)
Thus, the volume of the cone is 20π
Hence, Option C is the correct answer.