The top half of a storage tank is a circular cylinder that is 5 meters tall and has a diameter 2 meters. The bottom half of the tank is shaped like an 8-meter inverted cone (pointed down). Let h represent the depth of the tank's contents.

Question

At t = 0 minutes, a release valve at the bottom of the tank is opened and its contents flow out at a rate of 0.5 cubic meters per minute. Assuming the tank is completely full when the release valve is opened, answer the following:
a) Find the value of dh/dt when t = 30 minutes.
b) Find the value of dh/dt when h = 6 meters.

Answer 1

I am not going to do this because it is so long. However note that the change of volume per unit time is the surface area times the change of depth per unit time

dV/dt = pi r^2 dh/dt
so
5 = pi r^2 dh/dt

Answer 2

I mean
0.5 = pi r^2 dh/dt