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The sum of the surface areas of the r...

The sum of the surface areas of the rectangular parallelopiped with sides `x ,\ 2x` and `x/3` and a sphere is given to be constant. Prove that the sum of the volumes is minimum, if `x` is equal to three times the radius of the sphere. Also, find the minimum value of the sum of their volumes.

Text Solution

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The correct Answer is:
`18 r^(3)+(4)/(3) pi r^(3)`
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