State whether the following statement is True or False and justify your answer: If the radius of a cylinder is doubled and its height is halved,the volume will be doubled.

(TRUE) Let $r$ be the radius and $h$ be the height of the cylinder.
The original volume of the cylinder is given by $V_{1} = \pi r^{2} h$.
When the radius is doubled,the new radius becomes $2r$. When the height is halved,the new height becomes $\frac{h}{2}$.
The new volume $V_{2}$ is calculated as:
$V_{2} = \pi (2r)^{2} \times \left(\frac{h}{2}\right)$
$V_{2} = \pi (4r^{2}) \times \left(\frac{h}{2}\right)$
$V_{2} = 2 \pi r^{2} h$
$V_{2} = 2 V_{1}$
Since the new volume is twice the original volume,the statement is True.