SOLUTION: A sphere just fits inside a cube. What is the surface area of the sphere as a percentage of the surface area of the cube? Round your answer to the nearest whole percentage.

Question 1125545: A sphere just fits inside a cube. What is the surface area of the sphere as a percentage of the surface area of the cube? Round your answer to the nearest whole percentage.

Found 2 solutions by math_helper, FrankM:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Surface area of a sphere = where r=radius
Surface area of a cube = where a=length of one side

We need to relate r to a. Since the sphere just touches the sides of the cube, a = 2r.
So now we can write = =
is approximately 0.5236 so we can write the sphere has a surface area that is about 52% of the surface area of the cube.
Answer by FrankM(1040) (Show Source): You can put this solution on YOUR website!
The cube is a unit cube, with a side of 1 and a surface area of 6. (Right? Each side is 1x1 times 6 sides.)
The sphere, has a surface area of 4 pi r^2. The radius is 1/2 unit so
4 x pi x 1/4 or just pi.
sphere to cube is pi/6
or
3.14159/6 = .5236 just over 52% the surface area.
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