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

1 : 2 : 3

The correct answer is Option (1) → 1 : 2 : 3

For same base and height of Cone, cylinder and hemisphere,

height of cone and cylinder, h = radius of hemisphere, r = base radius of cone and cylinder, rb

Volume of Cone V1= \(\frac{1}{3}\)π \( {rb}^{2} \) h = \(\frac{1}{3}\)π \( {r}^{3} \)

Volume of hemisphere V2= \(\frac{2}{3}\)π \( {r}^{3} \) = \(\frac{2}{3}\)π \( {r}^{3} \)

Volume of Cylinder V3= π \( {rb}^{2} \) h = π \( {r}^{3} \)

V1:V2:V3 :: \(\frac{1}{3}\) : \(\frac{2}{3}\) : 1 = 1:2:3