PSAT Math Multiple-Choice Question 164: Answer and Explanation

Question: 164

SA = 4πr²

The formula for the surface area of a sphere with radius r is shown above. The radius of a volleyball is about 3 times the radius of a tennis ball. If a volleyball and a tennis ball are spherical, approximately how many times larger is the surface area of a volleyball than the surface area of a tennis ball?

• A. 3
• B. 9
• C. 27
• D. 36

Correct Answer: B

Explanation:

B

The question asks how many times larger the surface area of the volleyball is compared to the surface area of the tennis ball. Because the question does not ask for either surface area but only for the relationship between the two, this can be solved by plugging in. Plug in the radius of the tennis ball as 2. If r = 2, then SA = 4πr² = 4π(2)² = 16π for the tennis ball. The radius of the volleyball is three time the radius of the tennis ball, so, for the volleyball, plug in r = 3 × 2 = 6. If r = 6, then SA = 4πr² = 4π(6)² = 144π for the volleyball. Translate the question into an equation. The term how many translates to the variable. Use y. The word times translates to "multiplication." The term the surface area of the tennis ball translates to 16π. The word is translates to "equals." The term the surface area of a volleyball translates to 144π. Solve the equation y × 16π = 144π. Divide both sides by 16π to get y = 9. The correct answer is (B).