PSAT Math Multiple-Choice Question 527: Answer and Explanation

Question: 527

A company makes two different sizes of cylindrical paperweights with identical volumes. If the radius of Paperweight X is one-third the radius of Paperweight Y, then the height of Paperweight X is how many times the height of Paperweight Y?

• A. 9
• B. 3
• C.
• D.

Correct Answer: A

Explanation:

A

The question asks for the relationship between the heights of two cylinders of identical volume. The question involves a relationship between unknown numbers, so plug in. The question states the radius of Paperweight X is one-third the radius of Paperweight Y, so use r_X = 3 for Paperweight X and r_Y = 9 for the Paperweight Y. The formula for the volume of a cylinder is V = πr²h, so plug in the values to determine the volume of each cylinder. The volume of the Paperweight X is V = π(3)²hX = 9πh_X. The volume of Paperweight Y is V = π(9)²h_Y = 81πh_Y. Since the volumes are equal, set the equations equal to get 9πh_X = 81πh_Y. Divide both sides by 9π to get h_X = 9h_Y. Paperweight X's height will be 9 times that of Paperweight Y. The correct answer is (A).