Question

If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the new cylinder to that of the original cylinder.

Answer 1

Let $V_1$ be the volume of the original cylinder and $V_2$ be the volume of the new cylinder.
Radius of original cylinder$=$r, radius of new cylinder$=\frac{r}{2}$
$V_1=\pi r^{2}h$ and $V_2=\pi {\left(\frac{r}{2}\right)}^{2}h$
$\therefore \frac{V_1}{V_2}=\frac{\pi r^{2}h}{\pi \frac{r^2}{4}h}=\frac{4}{1}\Rightarrow \frac{V_2}{V_1}=\frac{1}{4}$
$\therefore V_2:V_1=1:4$.