Question

1. A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is being filled so that the depth of water is increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at which water is entering the reservoir when the depth is 5 feet.

Answer 1

dv = pi r^2 dh
where
r = (12/24)h = .5 h
so
dv = pi (.25)h^2 dh
dv/dt = .25 pi h^2 dh/dt
when h = 5
dv/dt = (25 pi/4 )dh/dt
dv/dt = (25 pi/4)(4)