# Filling up spheres

Calculus Level 5

A solid spherical tank of inner radius 3 m (thickness irrelevant) is being filled with water at a constant rate of $$\pi \: \:m^{3}/\text{min}$$ through a hole at its apex.

Determine how fast the level of the water is increasing (in $$m\: /min$$) at the instant the tank accumulates a volume of $$\large \frac{325}{24}\pi \: \text{m}^{3}$$ of water. Assume that the water level at any point on the surface is always equal, that is, no waves occur.

The rate can be expressed in the form $$\frac {A}{B}$$ where $$A$$ and $$B$$ are coprime integers. Input your answer as $$A + B$$.

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