# 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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