PSAT Math Multiple-Choice Question 221: Answer and Explanation

Question: 221

If a right cone is three times as wide at its base as it is tall, and the volume of the cone is 384π cubic inches, what is the diameter in inches of the base of the cone?

• A. 8
• B. 12
• C. 16
• D. 24

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Additional Topics in Math/Geometry

Getting to the Answer: If needed, don't forget to check the formulas provided for you at the beginning of each Math section. The volume of a right cone is given by . Here, you only know the value of one of the variables, V, so you'll need to use the information in the question to somehow write r and h in terms of just one variable. If the cone is three times as wide at the base as it is tall, then call the diameter 3 x and the height of the cone one-third of that, or x. The volume formula calls for the radius, which is half the diameter, or . Substitute these values into the formula and solve for x:

The question asks for the diameter of the base, which is 3 x = 3(8) = 24, choice (D).