Water is leaking out of an inverted conical tank at a rate of 9300 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height13 meters and the diameter at the top is 7meters. If the water level is rising at a rate of 21 centimeters per minute when the height of the water is 4meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Question

Water is leaking out of an inverted conical tank at a rate of 9300 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height13 meters and the diameter at the top is 7meters. If the water level is rising at a rate of 21 centimeters per minute when the height of the water is 4meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Recall that the volume of a right circular cone with height h and radius of the base r is given by V=1/3πr^2h

oobleck · Answer

using similar triangles, note that if the water depth is h, then the radius of the surface of the water is 7/26 h
So, now we have
v = π/3 (7h/26)^2 * h = 49π/2028 h^3
so that means that
dv/dt = 49π/676 h^2 dh/dt - 9300 = 49π/676 * 400^2 * 21 - 9300 = 755835 cm^3/min

check my math

susu · Answer

This looks wrong