Question

A rectangular beam is to be cut from a cylindrical log of diameter 10 inches. Show (using trig) that the maximum area will occur if we choose to cut a square. This problem uses similar ideas to the problem in the last homework. It's simpler in that we do not need calculus - we can solve it from beginning to end with the tools we are studying in this course. If you cannot start by writing a formula, start by making a table with different angles (30, 45, 60, 72.5 degrees, ...) We need to find an expression for length and width of the rectangles in terms of e. Then we use those expressions to construct an expression for the area of the rectangle. We then use an identity so the graph of the area is easy to understand.

Answer 1