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

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

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05 Aug 2019, 00:19
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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 18 Apr 2019 Posts: 78 Location: India GMAT 1: 720 Q48 V40 GPA: 4 Re: As the figure shows, a ball and cone are inscribed by a cylinder. What [#permalink] ### Show Tags 05 Aug 2019, 03:38 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 Math Revolution GMAT Instructor 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] ### Show Tags 07 Aug 2019, 02:15 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: As the figure shows, a ball and cone are inscribed by a cylinder. What  [#permalink]

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11 Aug 2019, 15:31
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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, 15:31