A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on?

each side through an angle 胃. How should 胃 be chosen so that the gutter will carry the maximum amount of water?


(answer in radians)A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on?
Drawing an altitude from a vertex gives you a height of 10sin@ and the longer side of the trapezoid 10cos@ +10 +10cos@ = 20 cos@ +10.


The median of the trapezoid is 10 +10cos@


Area is 10sin@(10 + 10 cos@) =100sin@ +100sin@cos@=


100sin@ +50sin2@


If you take the first derivative you get 100cos@ +100cos2@


Setting = 0, you will get @ =pi: disregard


and @ =pi/3