SOLUTION: what is the volume of the region inside a 6 inch cube but outside the sphere?
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Question 285377: what is the volume of the region inside a 6 inch cube but outside the sphere?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
what is the volume of the region inside a 6 inch cube but outside the sphere?
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Find the diagonal of the cube:
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hypotenuse of a face: 6*sqrt(2)
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diagonal = sqrt(6^2 + (6sqrt(2))^2)
diagonal = sqrt(36 + 72)
diagonal = 6sqrt(3)
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Therefore the radius of the sphere = (1/2)diagonal = 3sqrt(3)
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So the volume of the sphere = (4/3)(pi)(3sqrt(3))^3
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The volume of the cube = 6^3 = 216
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Volume within the sphere but outside the cube
= (4/3)pi(3sqrt(3)^3 - 216
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Cheers,
Stan H.
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