Question

A cone of radius 8 cm and height 12 cm is divided into two parts by a plane through the midpoint of its axis parallel to its base. Find the ratio of the volumes of two parts.

Answer 1

Let ORN be the cone then given, radius of the base of the cone r₁ = 8 cm

The plane along CD divides the cone into two parts, namely

(i) a smaller cone of radius 4 cm and height 6cm and (ii) frustum of a cone for which 

Radius of the top of the frustum, r₁ = 4 cm

Radius of the bottom,r₂ = 8 cm

and height of the frustum, h = 6 cm

∴ Required ratio = Volume of frustum : Volume of cone = 24 π: 32 π = 1:7