Posted by azis on Thursday, August 15, 2013 at 6:05am.
a long strip of sheet metal 12 inches wide is to be formed into an open gutter with a rectangular crosssection as shown. what is the maximum possible area of the crosssection?

spc  Reiny, Thursday, August 15, 2013 at 8:29am
Bend it down the middle and form into a trough with angle Ø
The area of the crosssection 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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