1. An animal feeding trough is to be made from a 2 meter strip of sheet metal that is 30 cm wide. The sheet metal is bent into an isosceles trapezoid by turning up strips that are x = 10 cm wide on each side so that they make the same angle, q, relative to a line perpendicular to the bottom. (See the figure below.)

a. Write the function of volume depending on q. Graph the volume as a function of the angle q as q varies from 0 to p/2.

b. Write the derivative of the volume function, V(q). Find the angle q and the width across the top that maximizes the volume of this trough. What is the depth and volume of the trough at this optimal solution?