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Math Help - Related Rates problem

  1. #1
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    Related Rates problem

    The ends of a water trough 8 feet long are equilateral triangle whose sides are 2 feet long. If water is being pumped into the trough at a rate of 5 ft^3/min, find the rate at which the water level is rising when the depth of the water is 8 inches.

    Thanks for your help.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by nystudent2729 View Post
    The ends of a water trough 8 feet long are equilateral triangle whose sides are 2 feet long. If water is being pumped into the trough at a rate of 5 ft^3/min, find the rate at which the water level is rising when the depth of the water is 8 inches.

    Thanks for your help.
    Recall that the area of an equilateral triangle is A=\frac{\sqrt{3}}{4}s^2, and its height is h=\frac{\sqrt{3}}{2}s, where s is the length of one of the sides. Thus, area can be written in terms of h as A=\frac{\sqrt{3}}{3}h^2

    So the volume of this trough is V=\frac{8\sqrt{3}}{3}h^2

    We know that \frac{\,dV}{\,dt}=5~\frac{ft^3}{min}. Thus, find \frac{\,dh}{\,dt}, when h is 8 inches [I would first convert this to feet]...

    Can you take it from here?

    --Chris
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