Question

A piece of wire 100 cm long is cut into two pieces. One piece is bent to form a square and the other to form a circle. Let x equal the length of the wire used to form the square.

A. write the function that represents the area of the two figures

B. determine the domain of the function

C. find the value(s) of x that yield a maximum and minimum area. Explain your reasoning.

Answer 1

the circumference of the circle is 100-x. So, the area is

a = (x/4)^2 + π((100-x)/2π)^2

This is just a parabola, so its vertex (minimum area) is easy to find.

For the maximum area, compare a at the ends of the domain.