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a long strip of sheet metal 12 inches wide is to be formed into an open gutter with a rectangular cross-section as shown. what is the maximum possible area of the cross-section?

  • spc -

    Bend it down the middle and form into a trough with angle Ø
    The area of the cross-section of the trough will be

    (1/2)(12)(12) sinØ
    = 72 sinØ
    d(area)/dØ = 72 cosØ
    = 0 for a max of area
    72 cosØ = 0
    cosØ = 0
    Ø = 90° or 270° , the last can be rejected

    So when Ø = 90°
    the area of the cross section will be
    (1/2)(12)(12)sin90 = 72 square inches

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