MH1810: A rain gutter is to be constructed from a metal sheet of width 30 cm by bending one-third of the sheet on each side through an angle: Math 1 Assignment, NTU, Singapore

Questions

1. A rain gutter is to be constructed from a metal sheet of width 30 cm
   by bending one-third of the sheet on each side through an angle θ: How
   should θ be chosen so that the gutter will carry a maximum amount of
   water? Express the answer in terms of π:
2. (a) Find the derivative of the function
   
   (b) Find the limit
   
3. (a) where the numbers a, b are to
   be determine.
   (b) A wedge is cut out of a circular cylinder of radius 3 by two planes.
   One plane is perpendicular to the axis of the cylinder. The other
   plane intersects the first plane at an angle of 60° along the diameter of
   the cylinder. Find the exact volume of the wedge.