A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio

Options

A. `1 : 2 : 3`
B. `2 : 1 : 3`
C. `2 : 3 : 1`
D. `3 : 2 : 1`

Answer

A

Explanation

Let R be the radius of each
Height of hemisphere = its radius = R cm
`:.` height of each = R cm
Ratio of their volumes `= ((1)/(3) pi R^(2) xx R) : ((2)/(3)pi R^(3)) : (pi R^(2) xx R)`