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Question
Find the ratio of the volume of a cube to that of a sphere which will fit inside it.
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Solution
Let the radius of the shere be R and the edge of the cube be a.
As the sphere is fit inside the cube .
so, diameter of the sphere =edge of the cube
⇒ 2R = a ...........(i)
Now,
The ratio of the cube to that of the sphere`= "Volume of the cube"/"Volume of the sphere"`
`=a^3/((4/3pi"R"^3))`
`=(2"R")^3/((3/4pi"R"^3))` [Using (i)]
`=(3xx8"R"^3)/(4pi"R"^3)`
`=6/pi`
`=6 : pi`
so,the ratio of the Volume of the cube to that of the sphere is 6 : π.
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