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Answer in the back of the book is wrong?

  1. Nov 18, 2014 #1
    I'm tutoring a kid in high school Calculus and his book gives an answer of (25√3)/4 for the following question.

    A trough of length 6m has a uniform cross-section which is an equilateral triangle with sides of length 1. Water leaks from the bottom of the trough at a constant rate of 0.1 m3/min. Find the rate at which the water level is falling at the instant when the water is 20cm deep.
     
  2. jcsd
  3. Nov 18, 2014 #2

    Ray Vickson

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    What is YOUR answer? Why do you think the book'a answer is wrong?
     
  4. Nov 18, 2014 #3
    The area of an equilateral triangle is A=h2/sqrt(3) if h is the height when it is standing on one of its tips
    ---->
    The volume of the trough in question is defined by the equation V=6*A=6*h2/sqrt(3)
    ---->
    dV = (12/sqrt(3))*h*dh by differentiation
    ---->
    dh = dv*(sqrt(3)/12)*(1/dh)
    --->
    dh = sqrt(3)/24 when dv=0.1 and h=0.2.

    Is this shoddy arithmetic by me, or am I a failure of a tutor, or both?
     
  5. Nov 18, 2014 #4

    Ray Vickson

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    I agree with your answer.
     
  6. Nov 18, 2014 #5
    I'm getting the same as you for m/min (except that dh/dt is negative). Are those the units requested?

    100 litres per minute is quite the leak.
     
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