A conical tank (as in Example 2) has height 8 m and radius 4 m at the base. Water flows in at a rate of 3 m³/min. Determine dh/dt as a function of h, and provide a graph of this relationship.

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EXAMPLE 2 Filling a Conical Container Water flows into a conical container at a rate of 5 in.³/s. Assume that the container has a height of 4 in. and a base radius of 2 in. Show that the rate that the water level is rising depends on the level of the water in the container, rising faster the higher the water level.