SAT Math Practice Question #1307 (Hard (700)) | Test Citadel
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SAT Math Difficulty: Hard (700)

Digital SAT Math Practice Question #1307

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A cylinder has a radius of $4$ inches and a height of $9$ inches. If the radius is increased by $50\%$ and the height is decreased by $50\%$, how does the volume of the cylinder change?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
⚡ 15-Second Desmos Speed Hack

Multiplier trick: Radius squared multiplier is $(1.5)^2 = 2.25$. Height multiplier is $0.5$. Total volume multiplier is $2.25 \times 0.5 = 1.125 \implies +12.5\%$.

Masterclass Solution & Distractor Trap Analysis

Original volume: $V_1 = \pi r^2 h = \pi(4^2)(9) = 144\pi$. New radius: $r_2 = 4 \times 1.5 = 6$. New height: $h_2 = 9 \times 0.5 = 4.5$. New volume: $V_2 = \pi (6^2)(4.5) = \pi(36)(4.5) = 162\pi$. Fractional change: $(162\pi - 144\pi) / 144...

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

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