# In a cylinder, if the radius is halved and the height is doubled, then the volume will be

Question:

In a cylinder, if the radius is halved and the height is doubled, then the volume will be
(a) the same
(b) doubled
(c) halved
(d) four times

Solution:

(c) halved

Suppose that the new radius is $\frac{1}{2} r$ and the height is $2 h$.

$\therefore$ Volume $=\pi \times\left(\frac{1}{2} r\right)^{2} \times 2 h$

$=\pi \times \frac{r^{2}}{4} \times 2 h$

$=\frac{1}{2} \pi r^{2} h$