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Question
A sphere of maximum volume is cut-out from a solid hemisphere of radius r, what is the ratio of the volume of the hemisphere to that of the cut-out sphere?
Solution
Since, a sphere of maximum volume is cut out from a solid hemisphere of radius.
i.e., radius of sphere
Therefore,
The volume of sphere
`=4/3 pi (r/2)^3`
`v_1 = 1/6pir^3`…… (i)
The volume of hemisphere `v_2 = 2/3pir^3` …… (ii)
Divide (i) by (ii).
`v_1/v_2 = (1/6 pir^3)/(2/3 pir^3)`
`=1/6 xx 3/2`
`v_1/v_2 = 1/4`
Hence , `v_2 :v_1 = 4:1`
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