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A metal sphere of radius 5cm is melted down and made into a solid cube. Find the length...

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christiano-cr7 | (Level 1) Salutatorian

Posted July 17, 2013 at 12:48 PM via web

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A metal sphere of radius 5cm is melted down and made into a solid cube. Find the length of a side of the cube.

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llltkl | College Teacher | (Level 3) Valedictorian

Posted July 17, 2013 at 1:29 PM (Answer #1)

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Volume of the metal sphere=`(4/3)*pi*r^3`

                                          =`(4/3)*pi*5^3`

Volume of a solid cube with length a= `a^3`

Since the volume of the metal emains same, so:

`a^3 = (4/3)*pi*5^3`

`rArr a=root(3)((4/3)*(22/7)*5^3)`

`rArr a=10root(3)(11/21)` =8.06104cm(approx.)

Therefore, the length of a side of the cube is approximately 8.06cm.

 

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