Mensuration

A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is

Answer

Given that the diameter of base = 8 ft

Therefore, radius of circular base = 8/2 = 4 ft

In triangle OAB and OCD

OA/AB = OC/CD

⇒ AB = (3 × 4)/12 = 1 ft

Volume of cone = 1/3 × π × r2 × h

Volume of remaining part = Volume of entire cone - Volume of smaller cone

= 1/3 × π × 42 × 12 - 1/3 × π × 12 × 3

= 1/3 × π × 189

= 198 cubic ft

The correct answer is 198.