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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 square region in terms of r?
$$A.\ \ \pi\cdot r^2$$
$$B.\ \ \pi\cdot r^2+10$$
$$C.\ \ \pi\cdot r^2+\frac{1}{4}\pi^2\cdot r^2$$
$$D.\ \ \pi\cdot r^2+\left(40-2\pi\cdot r\right)^2$$
$$E.\ \ \pi\cdot r^2+\left(10-\frac{1}{2}\pi\cdot r\right)^2$$
The OA is E.
Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
$$A.\ \ \pi\cdot r^2$$
$$B.\ \ \pi\cdot r^2+10$$
$$C.\ \ \pi\cdot r^2+\frac{1}{4}\pi^2\cdot r^2$$
$$D.\ \ \pi\cdot r^2+\left(40-2\pi\cdot r\right)^2$$
$$E.\ \ \pi\cdot r^2+\left(10-\frac{1}{2}\pi\cdot r\right)^2$$
The OA is E.
Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
