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Question
What is the ratio of the volume of a cube to that of a sphere which will fit inside it?
Solution
Ratio of sphere
`=1/2 xx "side of cube"`
`r = a/2`
Now,
Volume of cube `v_1 = a^3`
Volume of sphere
`v_2 = 4/3 pir^3`
`=4/3 pi(a/2)^3`
`=4/3 pi a^3 / 8`
`v_2 = 1/6pia^3`
The ratio of their volumes
`v_1 :v_2 = a^3 :1/6 pia^3`
`v_1 /v_2 = a^3/(1/6 pia^3)`
`=6/pi`
Hence, `v_1 :v_2 = 6 : pi`
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