Question

Check my work please!!! 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 derivative of h with respect to t when t = 30 minutes.

b) Find the value of derivative of Volume: 5pi = 15.71
31.42 minutes to drain
a)
v = pi r^2h
dv = pi r^2 dh
-.5 = pi dh
dh = -1/2pi m/min
b) h = 6
v = 1/3 pi r^2 h
When h =8, r =1,
When h = 6, r = 3/4
h = 8r, dh = 8 dr
dv = pi/3 (2rh dr + r^2 dh)
-1/2 = 9pi/16 dh
d