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.

Algebra ->  Distributive-associative-commutative-properties -> 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.       Log On


   

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) About Me  (Show Source):
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Surface area of a sphere = +4%28pi%29r%5E2+ where r=radius
Surface area of a cube = +6a%5E2+ 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 +4%28pi%29r%5E2+%2F+6%282r%29%5E2+ = +4%28pi%29r%5E2+%2F+%2824r%5E2%29+ = +pi+%2F+6+
+pi%2F6+ 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) About Me  (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.