Question

A CONE,HEMISPHERE,CYLINDER, STAND ON EQUAL BASES AND HAVE SAME HEIGHT. SHOW THAT THE VOLUME ARE IN RATIO 1:2:3

Answer 1

The formulas for the volumes of the solids are :

Cone:
V = 1/3 π R² H: R = radius of the base and H = the height of the cone
Base = π R²

Hemisphere:
V = 2/3 π R³ , R = radius
Base = π R²

Cylinder :
V = π R² H , R = radius and H is the height
Base = π R²

All of them have same base => Same Radius. They have same height too.
The height of a hemisphere is same as the radius. Hence, R = H.

So ratio of their volumes = 1/3 π R² H : 2/3 π R³ : π R² H
= R³ :2 R³ : 3 R³
= 1 : 2 : 3