Calculus

A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 80 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when the water is 30 cm deep?

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  1. dv = surface area * dh
    so
    dv/dt = surface area * dh/dt
    width at surface = 40 + (80-40)(30/40)
    = 40 + 30 = 70 cm = 0.70 m
    so
    surface area = 9 * .7 = 6.3 m^2
    so
    .3 m^3/min = 6.3 m^2 * dh/dt
    and
    dh/dt = .047 meters/min or 4.7 cm/min

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  2. A water trough is 6 m long and has a cross-section in the shape of an isosceles trapezoid that is 20 cm wide at the bottom, 80 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.2 m3/min how fast is the water level rising when the water is 20 cm deep?
    ____m/min

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