Question
A sphere of maximum volume is cut out from a solid hemisphere of radius r, The ratio of the volume of the hemisphere to that of the cut out sphere is :
Answer: Option B
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Volume of hemisphere = `2/3 pi r^3`
Volume of biggest sphere = Volume of sphere with diameter r = `4/3 pi (r/2)^3 = 1/6 pi r^3`
`:.` Required ratio = `(2/3 pi r^3)/(1/6 pi r^3) = 4/1` i.e. 4 : 1
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