PSAT Math Multiple-Choice Question 85: Answer and Explanation

Question: 85

Cone A and Cone B are both right circular cones with the same height. If the radius of Cone A is of the radius of Cone B, which of the following is the ratio of the volume of Cone A to the volume of Cone B?

• A. 27:64
• B. 9:16
• C. 3:4
• D. 4:3

Correct Answer: B

Explanation:

B

The question asks about the ratio of the volumes of two cones with different radii. The question also describes a relationship between unknown numbers, so plug in. The relationship between the radii of the cones is provided, so plug in numbers that fit this relationship. Plug in r = 6 for Cone A and r = 8 for Cone B. Let h = 3. The formula for the volume of a cone is , so plug in the values for r and h to determine the volume of each cone. The volume of Cone A is , and the volume of Cone B is . Therefore, the ratio of volume A to volume B is 36π:64π, which reduces to 9:16. The correct answer is (B).