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

  • math -

    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

  • math -

    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.

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