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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