The radius of a cylinder is increased by 120% and its height is decreased by 40%. What is the percentage increase in its volume?

Given : If the radius of a cylinder is increased by 120% and its height is decreased by 40%.

To find : What is the percentage change in the volume?

Solution :

Let r be the radius of cylinder is increased by 120%

i.e,$$\frac{220}{100}=\frac{11}{5}$$

The old radius is 5 and new radius is 11.

Let h be the height of cylinder is decreased by 40%

i.e,$$\frac{60}{100}=\frac{3}{5}$$

The old height is 5 and new height is 3.

The volume of old cylinder with r=5 and h=5

volume= $$\pi\ r^2h$$

=$$\frac{22}{7}\times\ 5^2\times\ 5=392.85$$

The volume of new cylinder with r=11 and h=3

volume =$$\frac{22}{7}\times\ 11^2\times\ 3=1140.85$$

Volume change is

1140.85-392.85=748

Percentage change is

$$\frac{748}{392.85}\times\ 100\ =\ $$

190.4%