What angle θ maximizes the cross-sectional area of the gutter? A rain gutter is made from sheets of metal 9 in. wide. The gutters have a 3-in base and two 3-in sides, folded up to an angle θ.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Top width of gutter = `3+2*3costheta`

 

Perpendicular distance between to and bottom = `3sintheta`

 

Cross sectional area (A) of the gutter = `(3+(3+2*3costheta))/2*3sintheta`

 

When the area is maximum then `(dA)/(d(theta)) = 0`

 

`A = (3+3+2*3costheta)/2*3sintheta`

`A = 9(1+costheta)*sintheta`

`A = 9(sintheta+costheta*sintheta)`

`A = 9/2(2sintheta+2sintheta*costheta)`

(The entire section contains 162 words.)

Unlock This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial
Approved by eNotes Editorial Team

Posted on