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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
As the figure shows, a ball and cone are inscribed by a cylinder. What  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 63% (02:33) correct 37% (03:17) wrong based on 49 sessions

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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 [ 57.4 KiB | Viewed 648 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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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
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: As the figure shows, a ball and cone are inscribed by a cylinder. What  [#permalink]

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=>

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 $$π(\frac{243}{2}) : π(\frac{243}{4}) : π(\frac{729}{4}) = 2 : 1 : 3.$$

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GMAT 1: 600 Q46 V27 Re: As the figure shows, a ball and cone are inscribed by a cylinder. What  [#permalink]

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1
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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You are missing on great learning if you don't know what this is: Project SC Butler Re: As the figure shows, a ball and cone are inscribed by a cylinder. What   [#permalink] 11 Aug 2019, 15:31

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