let the height of the water level be h m
let the radius of the water level be r m
we are told r/h = 1.75/13 = 7/52
52r = 7h
r = 7h/52
let the rate at which water is pumped be x m^3/min
V = (1/3)π r^2 h
= (1/3)π(49h^2/2704)h
= (49π/8112) h^3
dV/dt = (49π/2704) h^2 dh/dt
for our given data
x - .0142 = (49π/2704)(3.5)^2 (.17)
I get x = .1327562.. metres/min
check my arithmetic
Water is leaking out of an inverted conical tank at a rate of 0.0142 m3/min. At the same time water is being pumped into the tank at a constant rate. The tank has height 13 meters and the diameter at the top is 3.5 meters. If the water level is rising at a rate of 0.17 m/min when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank.
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