ACT Math Practice Question #2105 (Medium) | Test Citadel
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ACT Math Difficulty: Medium

Digital ACT Math Practice Question #2105

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A solid metal cylinder with radius 2 inches and height 6 inches is melted down and recast into a sphere. Assuming no metal is lost in the process, what is the radius of the sphere, in inches?
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Equate volumes: $24\pi = \frac{4}{3}\pi R^3 \implies R^3 = 18 \implies R = 18^{1/3}$.

Masterclass Solution & Distractor Trap Analysis

Volume of cylinder: $V_{cyl} = \pi r^2 h = \pi(2^2)(6) = 24\pi$. Set equal to sphere volume: $\frac{4}{3}\pi R^3 = 24\pi \implies \frac{4}{3}R^3 = 24 \implies R^3 = 24 \times \frac{3}{4} = 18 \implies R = \sqrt[3]{18}$....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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