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Calculus
Level
3
The sum of the surface areas of a cube and a sphere is a constant. The sum of their volumes is maximum when the ratio of the edge of the cube to the radius of the sphere is k. Find k
The answer is 0.
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1 solution
Well no need of calculus anywhere! For a given surface area, sphere has the maximum volume so we construct only the sphere and not the cube to get the maximum volume.Hence the ratio is 0.
P. S: You may need calculus to prove this statement"For a given surface area sphere has the maximum volume."