Question

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

Answer 1

Given:

A right circular cylinder

Let the radius be r

And the height be h

Solution:

Volume of the original cylinder= $\pi r^2h$

Volume of cylinder after radius is halved= $\pi (\frac{r} {2})^2h$

Ratio of the cylinder obtained to the volume of original cylinder

=$\frac{ \pi (\frac{r} {2})^2h} { \pi r^2h} \\\\\sf= \frac{ \pi (\frac{r^2} {4})h} { \pi r^2h} \\\\\sf =\frac {\pi r^2h}{4\pi r^2h } \\\\\sf =\frac {\cancel{\pi r^2h}}{4\cancel{\pi r^2h} } = 1/4= 1:4$

Ratio= 1:4