Write True or False and justify your answer in each of the following: $A$ cylinder and a right circular cone have the same base and the same height. The volume of the cylinder is three times the volume of the cone.

(TRUE) Let $r$ be the radius and $h$ be the height of both the cylinder and the right circular cone.
The volume of a cylinder is given by the formula $V_{cylinder} = \pi r^{2} h$.
The volume of a right circular cone is given by the formula $V_{cone} = \frac{1}{3} \pi r^{2} h$.
Comparing the two volumes,we can see that $V_{cylinder} = 3 \times (\frac{1}{3} \pi r^{2} h) = 3 \times V_{cone}$.
Therefore,the volume of the cylinder is indeed three times the volume of the cone.
Hence,the given statement is True.