Question

What is the ratio of the volume of the given right circular cone to the one obtained from it?
I. The smaller cone is obtained by passing a plane parallel to the base and dividing the original height in the ratio 1:2.
II. The height and base of the new cone are one-third those of the original cone.

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

For similar cones, volume ratio = cube of the linear ratio.

Answer 1

The Correct Option is B

From I: Ratio of heights is 1:2 → radius ratio = 1:2 (similar cones) → Volume ratio = $1^3 : 2^3 = 1:8$. Sufficient.
From II: Radius ratio = 1:3, height ratio = 1:3 → Volume ratio = $(1/3)^2 \times (1/3) = 1:27$. Sufficient.