please help me on this problem of my homework I am stomped. help ASAP

Question

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

Answer 1

There is a mix between meters and centimeters. 1 m = 100 cm

Given: h = 14 meters = 1400 cm

diameter = 6.5meters = 650 cm, r = 325 cm

leak = 14400 cm³/min

When h = 1400 cm, h' = 17 cm/min

Volume V = (1/3)πr²h

By similar triangles h/r = 1400/325 --> h = 4.3r and r' = 0.232h'

V= (1/3)πr²h = (1/3)πr³(4.3)

V' = 4.3πr²r'

When h = 450 cm, r = h/4.3 = 104.65 cm and r' = 0.232(17) = 3.95 cm/min

V' = 4.3π(104.65)²(3.95) = 584378 cm³/min

But we have to add the loss of 14400 cm³/min to compensate for the leak.

V' + leak = 598778 cm³/min