Question

A conical water tank with vertex down has a radius of 10 feet at the top and is 20 feet high. If water flows into the tank at a rate of 10 ft3/minft3/min, how fast is the depth of the water increasing when the water is 15 feet deep?

Answer 1

Since r=h/2 and V=(hpr^2)/3

V=(ph^3)/12

V(15)=281.25p and since V=10t, t=28.125p

V=(ph^3)/12

dV/dh=(3ph^2)/12=(ph^2)/4  and since V=10t, dV/dt=10

(dh/dV)(dV/dt)=dh/dt=12/(3ph^2)*10

dh/dt=120/(3ph^2)  and we want the rate when h=15 so

dh/dt(15)=120/(675p)

dh/dt=0.05658 ft/min