Assignment 8 W14: Problem 10 Previous Problem List Next (1 point) Water is leaki
ID: 2886004 • Letter: A
Question
Assignment 8 W14: Problem 10 Previous Problem List Next (1 point) Water is leaking out of an inverted conical tank at a rate of 14400 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 8 meters and the diameter at the top is 5.0 meters If the water level is rising at a rate of 20 centimeters per minute when the height of the water is 3.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute Your answer cubic centimeters per minuteExplanation / Answer
let radius of tank =r , height of tank = h
diameter at the top = 5m
=> radius at the top = 5/2 =2.5 meters
height of tank = 8 meters
r/h =2.5/8
=>r=(5/16)h
volume of tank ,V= (1/3)r2h
=>V= (1/3)((5/16)h)2h
=>V= (25/768)h3
rate of change of volume,dV/dt =(25/768)3h2(dh/dt)
=>dV/dt =(25/256)h2(dh/dt)
h=3meters=300cm, dh/dt =20 cm/min
net rate = rate of inflow-rate of outflow
=>rate of inflow-14400 =(25/256)*3002*20
=>rate of inflow=(25/256)*3002*20 +14400
=>rate of inflow=566633.1
water is being pumped into the tank at 566633.1 cubic centimeters per minute
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