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?
A. pi*r^2
B. pi*r^2 + 10
C. pi*r^2 + 1/4*pi^2*r^2
D. pi*r^2 + (40 - 2\pi*r)^2E. pi*r^2 + (10 - 1/2*pi*r)^2

E. pi*r^2 + (10 - 1/2*pi*r)^2

Step-by-step explanation:

Let the first cut piece be of length 'x'.

Let the second piece square be of length 'a'.

So, second piece length = Total length - first piece length

So, second piece length =

Now, the first piece is used to form a circle of radius 'r' while the second is used for a square of side length 'a'.

Circumference of the circle is equal to the length of the first piece.

So, ------ (1)

Area of circle is given as:

------- (A)

Now, perimeter of the square is equal to the length of second piece.

So,

Plug in 'x' value from equation (1) in equation (2). This gives,

Now, area of square is given as:

Now, total area is equal to the sum of the areas of circle and square. So,

Total area = Area of circle + Area of square

Total area =

Total area =

Therefore, option (E) is correct.

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step-by-step explanation: