Question

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1

Answer 1

let initially the radius and height of the cylinder be r and h respectively.

the volume of the cylinder , $V_1=\pi r^{2}h$

since the new radius is half the initial radius , new radius $=\frac{r}{2}$

the radius = h

the new volume of the cylinder $V_2=\pi (\frac{r}{2}{)}^{2}h=\frac{\pi r^{2}h}{4}$

therefore the ratio of the volume of the reduced cylinder to the original one is

$\frac{V_2}{V_1}=\frac{\frac{\pi r^{2}h}{4}}{\pi r^{2}h}=\frac{1}{4}$

thus the ratio is 1:4