Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 52 inches long and cuts it into two pieces. Steve takes the first piece of wire and bends it into the shape of a perfect circle. He then proceeds to bend the second piece of wire into the shape of a perfect square. What should the lengths of the wires be so that the total area of the circle and square combined is as small as possible

Steve should use:

Step-by-step explanation:

Let Steve cut the wire so that the first piece has length x.

Therefore, the second piece will have a length of (52 - x).

The wire of length x is used to make a circle

Circumference of a Circle,

The wire of length (52-x) is used to make a square.

Total Area = Area of Circle + Area of Square

Let us simplify the expression

This is the function of a parabola which opens up.

To find where A is minimum, find the axis of symmetry.

Steve should cut the wire so that the length of wire used to make a circle is 8.53 Inches.

Length of wire used to make the square =52-8.53=43.47 Inches

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