# Volume is Minimum

Calculus Level 3

The sum of the total surface area of a sphere with radius $$r$$, and a cuboid with sides $$x$$ , $$2x$$ and $$x/3$$ is constant. If the sum of the volume of the sphere and cuboid is minimum, then the value of $$r$$ can be expressed as $$r = \dfrac x{n+1}$$. Find $$n$$.

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