Spherplex

Geometry Level 4

A sphere of radius \(r\) is reconstituted into \(n\) smaller spheres, keeping the total volume constant.

Let \(a\) be the ratio of the total surface area of the smaller spheres to the surface area of the original sphere.

Let \(b\) be the ratio of the radius of the original sphere to the radius of the smaller sphere.

Let \(c\) be the ratio of the volume of the original sphere to the volume of the smaller sphere.

What is the minimum integer value of \(a + b + c\)?

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