Water is leaking out of an inverted conical tank at a rate of 500 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 10 meters and the diameter at the top is 4.5 meters. If the water level is rising at a rate of 26 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.
i know V=1/3pi r^2 h
i get: 413.5121 and it's not right, neither is 4135.121 or 41351.2 i don't know what im doing wrong.
No, that is not the volume of the tank. r varies with h in a cone. relate r to h, then make the Volume formula. From the height being 10 m, and r at the top is 4.5 m, then it appears that r= 4.5(h/10)
V=1/3pi [4.5(h/10)]^2 h
Take the derivative of that.
Then you know that dV/dt= ratein-rate out.
change the 500cm^2/min to m^3/min, so your dimensions are consistent.
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