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Question

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Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

Solution

Let V₁ and V₂ be the volume of the cube and sphere respectively, then
V₁= (2r)³ and V₂ =

4 over 3 comma space πr cubed

therefore space space space space straight V subscript 1 over straight V subscript 2 equals fraction numerator left parenthesis 2 straight r right parenthesis cubed over denominator begin display style 4 over 3 end style πr cubed end fraction equals fraction numerator 8 straight r cubed over denominator begin display style 4 over 3 end style πr cubed end fraction equals 6 over straight pi Hence comma space straight V subscript 1 space colon space straight V subscript 2 equals 6 space colon space straight pi

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