Water is leaking out of an inverted conical tank at a rate of 14300 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 12 meters and the diameter at the top is 3.0 meters. If the water level is rising at a rate of 15 centimeters per minute when the height of the water is 1.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Your answer: 21331.25 cubic centimeters per minute.
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Step 1: Determine the formula for the volume of a cone: \(V = \frac{1}{3} \pi r^2 h\), where \(r\) is the radius of the cone at height \(h\) and \(h\) is the height of the water in the tank. Show more…
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