SSAT Upper Level Quantitative · Question of the Day

SSAT Upper Level Quantitative Question of the Day

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Monday, September 7, 2026

A spherical balloon has a radius of 9 inches. If the radius is decreased by $\frac{1}{3}$ , by what factor does the volume decrease?

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Question of the Day

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A spherical balloon has a radius of 9 inches. If the radius is decreased by $\frac{1}{3}$ , by what factor does the volume decrease?

$\frac{1}{3}$
$\frac{8}{27}$
$\frac{27}{8}$ (correct answer)
$\frac{2}{3}$

Explanation: Original radius is 9 inches. Decreased by $\frac{1}{3}$ means the new radius is $9 - \frac{1}{3}(9) = 9 - 3 = 6$ inches. Original volume: $V_1 = \frac{4}{3}\pi(9)^3 = \frac{4}{3}\pi(729) = 972\pi$ . New volume: $V_2 = \frac{4}{3}\pi(6)^3 = \frac{4}{3}\pi(216) = 288\pi$ . The ratio of original to new volume is $\frac{V_1}{V_2} = \frac{972\pi}{288\pi} = \frac{972}{288} = \frac{27}{8}$ . So the volume decreases by a factor of $\frac{27}{8}$ . Choice A uses linear scaling. Choice B gives the reciprocal. Choice D incorrectly uses $\frac{2}{3}$ .