A conical water tank with vertex down has a radius of 12 feet at the top and is 28 feet high. If water flows into the tank at a rate of 30 ft^3/min, how fast is the depth of the water increasing when the water is 16 feet deep?

Answer 1

Make a sketch of a cross-section of the cone containing some water.
Let the radius of the circular water level be r ft, let the height of the water be h ft.
by similar triangles,
r/h = 12/28
28r = 12h
r = 3h/7

V = (1/3)πr^2 h
= (1/3)π(9h^2/49)h = (3/49)π h^3
dV/dt = (9/49)π h^2 dh/dt
fill in our data ...
30 = (9/49)π (16^2) dh/dt
30 =(2304/49 π) dh/dt
leaving it up to you to solve for dh/dt in ft/min

let me know what your answer is, will be here for another 20 min

Answer 2

I got .2031

Answer 3

correct , that is what I had