Please help me answer ASAP!! Find the rate at which water is pumped in cubic centimeters per minute.

Question

Water is leaking out of an inverted conical tank at a rate of 8300.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top is 6.5 meters. If the water level is rising at a rate of 18.0 centimeters per minute when the height of the water is 1.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. 

Note: Let "R" be the unknown rate at which water is being pumped in. Then you know that if V is volume of water, dV/dt = R - 8300.0. Use geometry (similar triangles?) to find the relationship between the height of the water and the volume of the water at any given time. Recall that the volume of a cone with base radius r and height h is given by 1/3(pi)r²h.

Round answer to the fourth decimal place.

(I have tried finding this answer multiple times but cannot get the right answer... Last answer I put was 139729.5296 and that is not correct...)

Answer 1

The cone has a height of 15 meters and diameter of 6.5 meters.

Due to similar triangles:

d = 6.5/15 * h

r = 13/60 * h Since radius is half the diameter.

Using the volume equation above.

V = 1/3 * π * r² * h

Substituting r

V = 1/3 * π * (13/60 h)² * h

V = 169πh³/(3600*3)

V = 169πh³/10800

Taking the derivative with respect to time of both sides yields.

dV/dt = 169πh²/3600 * dh/dt

Substitute h = 150 cm

dh/dt = 18 cm/min

dV/dt = 59729.5 cm³/min

Since there is an out flow of 8300 cm³/min

The inflow must be dV/dt + outflow.

59729.5+ 8300 = 63,029.5 cm³/min