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Water is leaking out of an inverted conical tank at a rate of 14000 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 14 meters and the diameter at the top is 5.5 meters. If the water level is rising at a rate of 15 centimeters per minute when the height of the water is 4.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Also, I let R be the unknown rate at which water is being pumped in and if is volume of water, and the volume of a cone with base radius r and height h is given by .
So here are my steps, but when ever I put in the answer it says it's incorrect. What am I doing wrong? Sorry about the work, I did this problem over three or more times, I don't have to show my work for the teacher too... units should be in cubic centimeters per minute.
Thanks,
Matt