PSAT Math Multiple-Choice Question 495: Answer and Explanation

Question: 495

V = πr²h

The formula for the volume, V, of a cylinder is given above, where r is the radius of the cylinder and h is the height of the cylinder. Which of the following gives the height of the cylinder in terms of its volume and radius?

• A. h = πVr²
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

The question asks for the height of a cylinder in terms of its volume and radius. There are variables in the answer choices, so plug in. Make r = 2 and h = 4. The volume becomes V = π(2)²(4) = V = 16π. The question asks for the equation to be solved for h, so the target value is 4. Now plug r = 2 and V = 16π into the answer choices to see which equation makes h = 4. Choice (A) becomes h = π(16π)(2²). Even without multiplying out the right side, this clearly will not make h = 4. Eliminate (A). Choice (B) becomes . Eliminate (B). Choice (C) becomes . Eliminate (C). Choice (D) becomes . This matches the target value of 4. The correct answer is (D).