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# Method to solve 3 spheres of dough problem

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Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 128

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Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Method to solve 3 spheres of dough problem [#permalink]

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30 Dec 2010, 00:06
Is the proper method to solving this problem: (1) find the volume of each sphere (2) add the volumes of the three spheres (3) calculate the radius from the new total volume?

There are three spheres of dough with diameters of 2, 4, and 6 cm. If the three are combined into one large sphere, what is the radius of the large sphere?

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Math Expert
Joined: 02 Sep 2009
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Re: Method to solve 3 spheres of dough problem [#permalink]

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30 Dec 2010, 01:51
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Expert's post
tonebeeze wrote:
Is the proper method to solving this problem: (1) find the volume of each sphere (2) add the volumes of the three spheres (3) calculate the radius from the new total volume?

There are three spheres of dough with diameters of 2, 4, and 6 cm. If the three are combined into one large sphere, what is the radius of the large sphere?

Yes, R^3=(2/2)^3+(4/2)^3+(6/2)^3:

$$volume_{sphere}=\frac{4}{3}\pi{r^3}$$;

$$volume \ of \ the \ large \ sphere=\frac{4}{3}\pi{1^3}+\frac{4}{3}\pi{2^3}+\frac{4}{3}\pi{3^3}=\frac{4}{3}\pi{(1^3+2^3+3^3)}$$;

$$volume \ of \ the \ large \ sphere=\frac{4}{3}\pi{(1^3+2^3+3^3)}=\frac{4}{3}\pi{R^3}$$ --> $$R^3=1^3+2^3+3^3=36$$.
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Ms. Big Fat Panda
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Re: Method to solve 3 spheres of dough problem [#permalink]

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30 Dec 2010, 00:27
Yep! That'd work

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Intern
Joined: 23 Oct 2010
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WE 1: Consulting - 1.5 Yrs
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Re: Method to solve 3 spheres of dough problem [#permalink]

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30 Dec 2010, 01:29
(2^3 + 3^3 + 6^3) = R^3

Don't know an easier way.

Posted from my mobile device

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Re: Method to solve 3 spheres of dough problem   [#permalink] 30 Dec 2010, 01:29
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