CAT 2020 Slot 1 QA Question 21: A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, th

Question

A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, th

Accepted Answer

The cut is parallel to the base. So, the small upper cone is similar to the original cone.

The original cone has height 27 cm. The cut is 18 cm from the base, so the small upper cone has height 9 cm.

Ratio of heights = $\dfrac{9}{27} = \dfrac{1}{3}$
Ratio of volumes = $\left(\dfrac{1}{3} \right)^

A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is