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InterviewSolution
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A solid hemisphsere is mounted on a solid cylinder, both having equla radii. If the whole solid is to have a fixed surface are and the maximum possible volume, then the ratio of the height of the cylinder to the common radius isA. `1:1`B. `1:2`C. `2:1`D. `sqrt(2):1` |
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Answer» Correct Answer - A `S=2 pi R^(2)+2 pi Rh +pi R^(2)` (R= radius of hemisphere & cylinder) `V=(2)/(3)pi R^(3)+piR^(2)H` `V=(2)/(3)pr R^(3)+ piR^(2)xx((5-3 pi R^(2))/(2 pi R))` `(dV)/(dR)= 2 pi R^(2)+(5)/(2)-(9 pi)/(2) R^(2)` For maximum & minimum `(dV)/(dR)=0` `5pi R^(2)=S` `5piR^(2)=3piR^(2)+2 piRh` `h:H=1:1` |
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