Tom N. answered • 05/09/19

Strong proficiency in elementary and advanced mathematics

Let leakout = 8900 cc/min. Height of the cone = 7m radius of the cone at top = 2.75m Volume of the cone

V = πr^{2}h/3. Using similar triangles in the cone r/2.75 =h/7 so r= 2.75h/7 now V= πh^{3}(2.75/7)^{2}/3 V=πh^{3}(.154).

V= .051πh^{3} and dV/dt = .153πh^{2}dh/dt where dh/dt = 18c/min. This now yields dV/dt = 175.2x10^{4}cc/min for the fill. To find the rate at which water is being pumped into the tank add the leak rate so that the rate is equal

to 1.75x10^{4} cc/min + .89x10^{4}cc/min which gives 176.09x10^{4} cc/min