SOLUTION: Find the surface area of the largest cube that can be cut from the sphere that has a radius of 5.00 cm.

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Question 765021: Find the surface area of the largest cube that can be cut from the sphere that has a radius of 5.00 cm.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the surface area of the largest cube that can be cut from the sphere that has a radius of 5.00 cm.
:
The diagonals to opposite corners of a cube that can be enclosed in the sphere
is the diameter 10 cm
:
Let s = the side of the cube
the diagonal of one side of the cube = sqrt%282s%5E2%29
the length of diagonals to opposite corners:
s^2 + (sqrt%282s%5E2%29)^2 = 10^2
s^2 + 2s^2 = 100
3s^2 = 100
s^2 = 100/3
That is also the area of one side of the cube, therefore
6%28100%2F3%29 = 200 is area of the enclosed cube