Surface of a cube with an edge equals to the surface of a sphere with a radius . What must be the ratio equal to?
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The surface area of a cube is given by S c = 6 a 2 where a is the side length. The surface area of a sphere is given by S s = 4 π r 2 where r is the radius. Since the surface areas are equal, we have
6 a 2 = 4 π r 2
Dividing both sides by 6 r 2 , we get
r 2 a 2 = 6 4 π
Extracting the square root of both sides, we get
r a = 6 2 π
Rationalizing the denominator by multiplying the above result by 6 6 , we get
r a = 3 6 π