water is leaking out of an inverted conical tank at a rate of 7100.000 cubic centimeters per min?

water is leaking out of an inverted conical tank at a rate of 7100.000 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. the tank has height 12.000 meters and the diameter at the top is 5.000 meters. if the water level is rising at a rate of 28.000 centimeters per minute when the height of the water is 4.500 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

no data is given about the rate that the radius is changing as a function of time (that is dr/dt).
 
examining the 2-d version of the inverted cone, slicing it in half along the height,  the height is 1200 cm when the radius is 250 cm as given in the problem. so for any given height h, the radius at that height forms two similar right triangles.
 
the proportion is h/1200 = r/250 -->  r = 5*h/24
 
 
substituting this into the formula for the volume of the cone:
   v = 1/3*pi* r^2*h = 1/3*pi* (5/24h)^2 * h = 1/3*pi* 25/576*h^3
 
 
taking the derivative of both sides:
 
 dv/dt = pi * 25/576*h^2* dh/dt
 
 
as given in the problem, dv/dt = c - 7100 for some fixed constant we are trying to find.
 
h = 4.5m = 450 cm when dh/dt = 28 cubic centimeters per min
 
the equation becomes:
 
c-7100 = pi * 25/576 * 450 ^2 * 28
 
solving for c and using pi=22/7 gives a result of 780537.5 cubic centimeters per minute or .7805575 meters per minute.
 
at this rate the tank will fill in just over minutes