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Question
A sphere and a cube have equal surface areas. What is the ratio of the volume of the sphere to that of the cube?
Solution
Surface area of sphere = sphere area of cube
i.e., 4πr2 = 6a2
`r^2/a^2 = 6/(4pi)`
`r/a = (6/(4x))^(1/2)`…… (i)
`"Now" , "volume of sphere"/"volume of cube" = (4/3pir^3)/a^3`
`v_1 /v_2 = (4pir^3)/(3a^3)`
`=4/3 pi(r/a)(r/a)^2`
`=4/3 pisqrt(6/pi) 1/2 6/pi`
`v_1/ v_2 = sqrt(6/pi)`
`v_1 :v_2 = sqrt(6/pi)`
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