A thin piece of 40 m wire is cut in two. One piece is a circle with radius of r. Other is a square. No wire is left over. Which represents total area of circle and square in terms of r?
From a 40m rope, two equal parts of 20 represent, respectively, the circumference of Circle C and the perimeter of Square D.
1. Express the perimeter of D in terms of the circumference of C.
Perimeter + Circumference = 40
Perimeter = 40 - C
2. Substitute accepted identities for perimeter and circumference.
4s = 40 - 2(pi)(r)
3. Express the side of the square in terms of r.
s = 10 - (pi)(r)/2
4. Write area of circle and square in terms of r.
Area(C) + Area(D)
= (pi)(r)^2 + s^2
= (pi)(r)^2 + (10 - (pi)(r)/2)^2
2(pi)(r) = 20
r = 10/pi
= 3.18 (approx. to hundredth)
s = (10 - (pi)(r)/2)
= 10- [3.14(3.18)]/2
The actual value of the side of the square derived from stating area of square in terms of r is consistent with its known perimeter.Posted from my mobile device