jee-main 2022 Q73

jee-main · India · session1_26jun_shift2 Stationary points and optimisation Geometric or applied optimisation problem

Consider a cuboid of sides $2 x , 4 x$ and $5 x$ and a closed hemisphere of radius $r$. If the sum of their surface areas is constant $k$, then the ratio $x : r$, for which the sum of their volumes is maximum, is
(1) $2 : 5$
(2) $19 : 45$
(3) $3 : 8$
(4) $19 : 15$

Consider a cuboid of sides $2 x , 4 x$ and $5 x$ and a closed hemisphere of radius $r$. If the sum of their surface areas is constant $k$, then the ratio $x : r$, for which the sum of their volumes is maximum, is\\
(1) $2 : 5$\\
(2) $19 : 45$\\
(3) $3 : 8$\\
(4) $19 : 15$

Paper Questions

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