Water is leaking out of an inverted conical tank at a rate of 11600.011600.0 cubic centimeters per min at the same time that wat
er is being pumped into the tank at a constant rate. The tank has height 13.013.0 meters and the diameter at the top is 5.05.0 meters. If the water level is rising at a rate of 22.022.0 centimeters per minute when the height of the water is 4.04.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute
1 answer:
Answer:
Win=436584.2477 cm3/min
Step-by-step explanation:
Volume for a conical tank
V=π/3 r^2 h
We need a relation between r and h
r/h=252.5/1301.3=0.194 --> r=0.194h
sust. in Volume equation
V=π/3 (0.194r)^2 h=0.0394h^3
taking derivative with time respect in both sides
dV/dt=3(0.0394) h^2 dh/dt and we know when h=404cm, dh/dt=22.022 cm/min
dV/dt=3(0.0394)(404)^2 (22.022)=424984.2477 cm^3/min
Also, we know
dV/dt=Win-Wout and Wout=Win-11600.01160
Finally
Win=424984.2477+11600.0116
Answer
Win=436584.2477 cm3/min
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