Question

minimizing area: A 36-in. piece of wire is cut into two pieces. One Piece is used to form a circle while the other is used to form a square. How should the wire be cut so that the sum of the areas is minimal? What is the minimum value?

Answer 1

The sum of the areas is\[A(r)=\frac{1}{2}(2\pi)r^2 + (36-2\pi r)^2\]You want this to be a \(\textit{minimum}\). This will happen when the first derivative of A = 0. (though this could also be a maximum. To figure out which, you'd need the second derivative I think).

Answer 2

what do i do next?

Answer 3

That should get you a value for r.

Answer 4

Then you work out the length \(2\pi r\), and the length \((36 - 2\pi r)\)