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.
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.
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.
Show Hint
For similar cones, volume ratio = cube of the linear ratio.
Updated On: Aug 6, 2025
- The question can be answered by one of the statements alone but not by the other.
- The question can be answered by using either statement alone.
- The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
- The question cannot be answered even by using both statements together.
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
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.
From II: Radius ratio = 1:3, height ratio = 1:3 → Volume ratio = $(1/3)^2 \times (1/3) = 1:27$. Sufficient.
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