CAT 2018 Slot 1 QA Question 16: 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 $\pi = \dfrac

Question

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 $\pi = \dfrac

Accepted Answer

The original cone has height 12 ft and radius 4 ft.
The plane is 9 ft from the base, so the small cone cut off at the top has height 3 ft.
By similarity, the radius of the small cone is
$\dfrac{4 	imes 3}{12} = 1$ ft.
Volume of original cone $=\dfrac{1}{3} 	imes \pi 	imes 4^{2} 	imes 12 = 64\pi$

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=227\pi = \dfrac{22}{7}π=722​, the volume, in cubic ft, of the remaining part of the cone is

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 $\pi = \dfrac{22}{7}$ , the volume, in cubic ft, of the remaining part of the cone is