Mathematics

Problem

A right circular cone with its tip down has a height of

15\,\text{m}

and a base radius of

6\,\text{m}

. Water in the cone currently has a depth of

4\,\text{m}

, and the depth is increasing at a rate of

0.03\,\text{m/min}

. Determine the instantaneous rate at which the radius of the circular water surface is changing at that moment. Clearly indicate units and whether the radius is increasing or decreasing.

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