SOLUTION: a sphere has a surface area of 64 p.i. find the surface area of the largest cube contained in the sphere

Question 766564: a sphere has a surface area of 64 p.i. find the surface area of the largest cube contained in the sphere

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a sphere has a surface area of 64 p.i. find the surface area of the largest cube contained in the sphere
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SA = 4*pi*r^2 = 64
r^2 = 16pi
r = 4sqrt(pi)
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Diagonal of the cube = 8*sqrt(pi)
Diagonal of the base of the cube = (8sqrt(pi))/sqrt(2) = 8sqrt(pi/2)
Edge of the cube = (8sqrt(pi/2))/sqrt(2) = 8sqrt(pi/4) = 4sqrt(pi)
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Surface area of the cube = 6(4sqrt(pi))^2 = 6(16pi) = 96pi sq units
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Cheers,
Stan H.
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