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Question
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
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Solution
Let edge of the cube = a
Volume of the cube = a × a × a = a3
The sphere, which exactly fits in the cube, has radius = `a/2`
Therefore, volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx (a/2)^3`
= `4/3 xx 22/7 xx a^3/8`
= `11/21 a^3`
Volume of cube : Volume of sphere
= `a^3 : 11/21 a^3`
= `1 : 11/21`
= 21 : 11
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(Use π = `22/7`)
