A cylindrical water tank is being filled with a hose. The depth of the water increases by 1 1/4 ft per hour. How many hours will it take for the water level in the tank to be 3 1/2 ft deep?
A water tank has the shape of an inverted right circular cone with an altitude of 12ft and
a base radius of 6ft. If water is being pumped into the tank at a rate of 10 gal/min(1.337
f t3/min, approximate the rate at which the water level is rising when the water is 3 ft deep.
h
r
12
6
We know dv
dt = 1.337, h = 3. We also
have the relationship between h and r by using similar triangles.
r
h = 6
12
or that r = 1
2h
V = 1
3πr2h = 1
3π
1
2h
2
h = 1
12πh3
dV
dt = 1
4
πh2 ∗
dh
dt now plug in the info and solve for dh
dt
Answer: dh
dt = .1891f t/min
