Question

You are asked to express one variable as a function of another. Be sure to state a domain for the function that reflects the constraints of the problem.

A piece of wire 13 inches long is cut into two pieces. The first piece is bent into a circle, the second into a square. Express the combined total area of the circle and the square as a function of x, where x denotes the length of the wire that is used for the circle.

A(x)= ?

Answer 1

I really don't know if I'm on the right track with this, but these are my thoughts. If the length of wire is cut in two then bent into a circle and square, then the length is 2(pi)(x) + 4x. If the total length must be less than or equal to 13, then solving for x I got: x <= 13/(2(pi)+4). The question asked for a function of area though, so I plugged in x to the area of a circle + the area of a square. A(x) = x^2(pi + 1); for x <= 13/(2(pi)+4).

Again, I was just playing around, and I'm highly suspicious of my answer. Hopefully it will give you some inspiration on how to solve it for real.