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Math Help - Rain Gutter Problem (Optimization)

  1. #1
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    Rain Gutter Problem (Optimization)

    Hello: I am a first year Calc Student and am having a bit of trouble with an application problem:
    The problem asks me to find the best shape for a rain gutter (in terms of how much volume will flow down it). We are given three shapes to test (A half circle, Triangle, and Square) Total length of metal used (and bent into these shapes was 10 cm)
    There are three different questions here (optimization of area of half circle, square and triangle) any help would be great!


    I believe there are three seperate questions here, I suppose the point of this entire question was to find which shape has the most area (and thus flow throught it) Calculus MUST be Used!

    Thanks
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  2. #2
    Junior Member eddie2042's Avatar
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    Quote Originally Posted by CalculusNewb1986 View Post
    Hello: I am a first year Calc Student and am having a bit of trouble with an application problem:
    The problem asks me to find the best shape for a rain gutter (in terms of how much volume will flow down it). We are given three shapes to test (A half circle, Triangle, and Square) Total length of metal used (and bent into these shapes was 10 cm)
    There are three different questions here (optimization of area of half circle, square and triangle) any help would be great!


    I believe there are three seperate questions here, I suppose the point of this entire question was to find which shape has the most area (and thus flow throught it) Calculus MUST be Used!

    Thanks
    Ok simply get the area and perimeter functions for each shape. Relate the two, then differentiate the area function with respect to the length parameter. Set it equal to zero and solve for the dimensions. Find the one with the largest area.

    Show us what you can do.
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