Question

The radius of the base of a circular cylinder is halved and height is doubled. Find the percentage change in the volume.

Answer 1

For original Cylinder:
Radius$=r$
Height $=h$
Volume$=\pi \times r\times r\times h$

For new Cylinder:
Radius $=\frac{r}{2}$
Height $=2h$
Volume $=\pi \times \frac{r}{2}\times \frac{r}{2}\times 2h$

​Therefore, Required Ratio $=$ New Cylinder $:$ Original Cylinder
$=(\pi \times \frac{r}{2}\times \frac{r}{2}\times 2h):(\pi \times r\times r\times h)$
$=\frac{1}{2}$
$=\frac{1}{2}\times 100\%$
$=50\%$