Water is flowing at a rate of 10 m3/s into the cylindrical tank shown below.

Question

a) Find the volume V of the water as a function of the water level h.
b) Find h as a function of the time t during which water has been flowing into the tank.

height of cylinder: 80m
height of water: ?
diameter of cylinder: 40m

Answer 1

V = pi r^2 h

dV/dt = pi r^2 dh/dt = 10 m^3/s

so
dh/dt = 10/(pi r^2)
h = 0 + [ 10/(pi r^2) ] t

Answer 2

Andrew’s car starting at 12:00 noon travels west at a speed of 30 kph. Andrei’s car starting from the same point at 2:00 pm travels north at 45 kph. Find how fast the two are separating at 4:oopm.