Water flows into a conical vessel 18 cm deep and 6 cm in radius at the rate of 0.2 cm³/sec. When the water level is 9 cm deep, find the rate at which the water surface of the vessel is increasing.

When the water is 9 cm deep, the radius of the water surface is half the vessel radius, making it 3 cm, so the area is pi times 3 squared or 9 pi. The rate of increase of the water level equals the flow rate divided by the surface area, which is 0.2 divided by 9 pi. Simplifying the fraction 1 divided by 5 divided by 9 pi gives a rate of 1/(45 pi).

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