SOLUTION: i have to find the radius of a hollow sphere The metal in the sphere is 3cm thick and the volume of the metal is 684 times pi cm cubed.

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Question 284014: i have to find the radius of a hollow sphere
The metal in the sphere is 3cm thick and the volume of the metal is 684 times pi cm cubed.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
i have to find the radius of a hollow sphere
The metal in the sphere is 3cm thick and the volume of the metal is 684 times pi cm cubed.
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Volume of a sphere = 4%2Api%2Ar%5E3%2F3
The volume of the 3 cm wall is the volume of a sphere of radius (r+3) minus a sphere or radius r.
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684%2Api+=+%284%2Api%2F3%29%2A%28%28r%2B3%29%5E3+-+r%5E3%29
684+=+%284%2F3%29%2A%28r%5E3+%2B+9r%5E2+%2B+27r+%2B+27+-+r%5E3%29
171+=+%281%2F3%29%2A%289r%5E2+%2B+27r+%2B+27%29
171+=+3r%5E2+%2B+9r+%2B+9
57+=+r%5E2+%2B+3r+%2B+3
r%5E2+%2B+3r+-+54+=+0
(r + 9)*(r - 6) = 0
r = 6 cm (inside radius)
r = 9 cm (outside radius)