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As the figure shows, a ball and cone are inscribed by a cylinder. What

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As the figure shows, a ball and cone are inscribed by a cylinder. What  [#permalink]

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New post 05 Aug 2019, 01:19
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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?

Attachment:
8.5 PS.png
8.5 PS.png [ 57.4 KiB | Viewed 455 times ]


\(A. 1:1:2\)

\(B. 1.5:1:3\)

\(C. 1.5:1.5:2\)

\(D. 2:1:3\)

\(E. 3:2:4\)

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Re: As the figure shows, a ball and cone are inscribed by a cylinder. What  [#permalink]

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New post 05 Aug 2019, 04:38
This question is pretty straight forward if you know the formulas and realize that the diameter of the sphere is equal to the height of the cone and cylinder.

Vol of sphere : 4/3*(pi)*r^3

Vol of cone : 1/3*pi*r^2*h

Vol of cylinder : pi*r^2*h

pi and r^2 pretty much cancel right away. 2r = h (as mentioned above)
therefore, we get - 2:1:3
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Re: As the figure shows, a ball and cone are inscribed by a cylinder. What  [#permalink]

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New post 07 Aug 2019, 03:15
=>

From the figure, the radii of the sphere and the base circle are \((\frac{9}{2})\).

The volume of the sphere is \((\frac{4}{3}) π(\frac{9}{2})^3 = π(\frac{243}{2}).\)

The volume of the cone is \((\frac{1}{3}) π(\frac{9}{2})^2(9) = π(\frac{243}{4}).\)

The volume of the cylinder is \(π(\frac{9}{2})^2(9) = π(\frac{729}{4})\)

Thus, the volumes are in the ratio \(π(\frac{243}{2}) : π(\frac{243}{4}) : π(\frac{729}{4}) = 2 : 1 : 3.\)

Therefore, the answer is D.
Answer: D
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Re: As the figure shows, a ball and cone are inscribed by a cylinder. What  [#permalink]

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New post 11 Aug 2019, 16:31
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MathRevolution wrote:
[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?

Attachment:
8.5 PS.png


\(A. 1:1:2\)

\(B. 1.5:1:3\)

\(C. 1.5:1.5:2\)

\(D. 2:1:3\)

\(E. 3:2:4\)


If you know for a fact that volume of a cone is 1/3rd of the volume of the cylinder then you can just compare ratios.
In case of D, Cylinder is 3/6 which is 1/2.
1/3 of 1/2 is 1/6. Option D satisfies that.
Hence D.

I got it right but I did not approach it correctly.
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Re: As the figure shows, a ball and cone are inscribed by a cylinder. What   [#permalink] 11 Aug 2019, 16:31
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