A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?
We make a circle with radius r: the area is Pi*r^2.
How much wire is left? The wire we used for the circle is equal to the circumference of the circle: 2r*Pi. We have 40 - 2r*Pi meters of wire with which to make the square. Thus, 40 - 2r*Pi will be the perimeter of the square, and each side will be one quarter that length: 10 - 0.5r*Pi. The area of the square will be (10 - 0.5r*Pi)^2, and if you add that to Pi*r^2, you'll get the answer.
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