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Method to solve 3 spheres of dough problem

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Method to solve 3 spheres of dough problem [#permalink]

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New post 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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Re: Method to solve 3 spheres of dough problem [#permalink]

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New post 30 Dec 2010, 01:51
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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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Re: Method to solve 3 spheres of dough problem [#permalink]

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

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Re: Method to solve 3 spheres of dough problem [#permalink]

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

Don't know an easier way.

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

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