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Answer on Calculus Question for hsd

Question #17240
Water is leaking out of an inverted conical tank at a rate of 10,000cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6m and the diameter at the top is 4m. If the water level is rising at a rate of 20cm/min when the height of the water is 2m, find the rate at which water is being pumped into the tank.

=................cm^3/min
Expert's answer
The tank has square S= (PI*d^2)/4 = 9*PI m^2
V_tot = V_in - V_out=S*2 = 18*10^3*PI cm^3/min
So, V_in = 28,000 cm^3/min

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