Question

A cone, a hemisphere and a cylinder stand on equal bases and have the same height What is the ratio of their respective volumes ?

Answer 1

Let the volume of the cone, hemisphere, and cylinder be $V_1,V_2,V_3$

Let the radius of the cone, hemisphere, and cylinder be $r$

$\therefore$ hight of the hemisphere is also $r$

$\therefore$ $V_1:V_2:V_3=\frac{1}{3}\pi r^2.r:\frac{2}{3}\pi r^3:\pi r^2.r$

$\frac{1}{3}:\frac{2}{3}:1$

$=1:2:3$