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As the figure shows, a ball and cone are inscribed by a cyli

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by Max@Math Revolution » Mon Aug 05, 2019 12:02 am
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[GMAT math practice question]

As the figure shows, a ball and cone are inscribed by a cylinder. What is the ratio of the volumes of the sphere to the cone to the cylinder?

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A. 1:1:2
B. 1.5:1:3
C. 1.5:1.5:2
D. 2:1:3
E. 3:2:4
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by Max@Math Revolution » Wed Aug 07, 2019 1:57 am
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From the figure, the radii of the sphere and the base circle are (9/2).
The volume of the sphere is (4/3) π(9/2)^3 = π(243/2).
The volume of the cone is (1/3) π(9/2)^2(9) = π(243/4).
The volume of the cylinder is π(9/2)^2(9) = π(729/4)

Thus, the volumes are in the ratio π(243/2) : π(243/4) : π(729/4) = 2 : 1 : 3.

Therefore, the answer is D.
Answer: D
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