Question

Find the ratio of the volumes of a cone and of a cylinder whose base diameter and heights are equal.

Answer 1

Given based and hegight of cylinder & cone are equal.

Let "h" be height cand 'y' be radius of base then

Volume of cylinder $\left(V_1\right)=\pi r^{2}h$

&

Volume of cone $\left(V_2\right)=\frac{1}{3}\pi r^{2}h$

then $\frac{V_2}{V_1}=\frac{1}{3}\frac{\pi r^{2}h}{\pi r^{2}h}=\frac{1}{3}$

$\therefore$ ratio of volume of cone to that of cylinder is $1:3$