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Math Help - Depth

  1. #1
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    Depth

    A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
    (a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.3 foot deep?

    _________ ft/min
    (b) If the water is rising at a rate of inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough.

    _________ ft3/min
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  2. #2
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    Quote Originally Posted by tradar View Post
    A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
    (a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.3 foot deep?

    _________ ft/min
    (b) If the water is rising at a rate of inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough.

    _________ ft3/min
    you need to get the volume, V, of water in the trough as a function of its depth, h.

    V = (area of end triangle)(trough length)

    V = \frac{1}{2}bh \cdot 12 = 6bh

    note from the figure that b = h ...

    V = 6h^2

    take the time derivative and answer the questions.
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