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:

(a) Find the derivative of the function (b) Find the limit

(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.