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

## Answer this Question

## Related Questions

- pre-calc - construction of a rain gutter: a piece of rectangular sheet metal is ...
- mathematics - Please help me answer this question; 1.A metal gutter open at the ...
- geometry - a piece of rectangular sheet metal is 20 in. wide. It is made into a ...
- Math Wrod Problem - 1. A long strip of copper 8 inches wide is to be made into a...
- Pre-Calc) - a piece of rectangular sheet metal is 20 in wide. It's to be made ...
- Differential calculus - A gutter with trapezoidal cross section is to be made ...
- calculus - A long rectangular sheet of metal, 12 inches wide, is to be made into...
- Calculus - A long rectangle sheet of metal, 15 inches wide is to be made into a ...
- CALCULUS - 1. A rectangular package to be sent by a postal service can have a ...
- maths - the cross section of a canal is a trapezium in shape .if the canal is ...

More Related Questions