SOLUTION: A sphere and a cube have same volume. Find the ratio of the lenght of the side of the cube to the radius of the sphere.

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Question 443127: A sphere and a cube have same volume. Find the ratio of the lenght of the side of the cube to the radius of the sphere.
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
As you know the volume of the sphere with radius r is:V%5B1%5D=%284%2F3%29%28pi%29r%5E3, and
the volume of the cube with length a is:V%5B2%5D=a%5E3.
To find the ratio a%2Fr, we know that V%5B2%5D=V%5B1%5D, substituting:
a%5E3=%284%2F3%29%28pi%29r%5E3=> a%5E3%2Fr%5E3=4%2A%28pi%29%2F3 => %28a%2Fr%29%5E3=4%2A%28pi%29%2F3, and,
a/r=cubed root of 4%2A%28pi%29%2F3 or a%2Fr=%284%2A%28pi%29%2F3%29%5E%281%2F3%29=1.66