A piece of wire 3 m long is cut into two pieces.

Question

One piece is bent into the shape of a circle of radius  and the other is bent into a square of side . How should the wire be cut so that the total area enclosed is:

a) a maximum? r=_____ and s=______

b) a minimum? r=_____ and s=______

Answer 1

Use the formulas for the area of circle and the area of a square. First, determine the circumference of the circle and the perimeter of the square. Ultimately, you want each area formula to be expressed in terms of r and s. To find the maximum and minimum area, you will need to differentiate the functions and find the critical numbers.