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 cross-section as shown. what is the maximum possible area of the cross-section?

- spc -
**Reiny**, Thursday, August 15, 2013 at 8:29am
Bend it down the middle and form into a trough with angle Ų

The area of the cross-section of the trough will be

(1/2)(12)(12) sinŲ

= 72 sinŲ

d(area)/dŲ = 72 cosŲ

= 0 for a max of area

72 cosŲ = 0

cosŲ = 0

Ų = 90° or 270° , the last can be rejected

So when Ų = 90°

the area of the cross section will be

(1/2)(12)(12)sin90 = 72 square inches

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