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. 
:
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(2s^2)}}}
the length of diagonals to opposite corners:
s^2 + ({{{sqrt(2s^2)}}})^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(100/3)}}} = 200 is area of the enclosed cube