Water is leaking out of an inverted conical tank at a rate of 6700.0 cm³/min at the same time that water is being pumped into the tank at a constant rate.

Question

Water is leaking out of an inverted conical tank at a rate of 6700.0 cm³/min at the same time that water is being pumped into the tank at a constant rate. The tank has a height of 15.0 m and the diameter at the top is 4.5 m. If the water level is rising at a rate of 23.0 cm/min when the height of the water is 2.0 m, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Answer: ? cm³/min

Answer 1

Let Qout=6.7 m³/min and dh/dt=23 @h=2 Note that h =6r where r=radius of tank so dr/dt=23/6 and r=1/3 at h=2 The volume of water in the tank = V=πr²h/3 or 2πr³/3. Note that dV/dt=Qin-Qout=2πr²dr/dt substitute and solve for Qin to find Qout=2π/27+6.7 m³/min