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?

Question

Mathematics

Gizmo

19 January, 07:35

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?

+5

Answers (1)

Know the Answer?

Louisa · 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