### Instruction: A piece of wire 72 cm long is cut into two equal pieces and each is formed into a circle. What is the sum, in square centimeters, of the areas of these circles?### Response: I need to find the areas of the circles, so I need to know their radii.
The wire is cut into two equal pieces, so each piece has length 36 cm.
The length of the wire is the same as the circumference of the circle, so I can use the formula C = 2πr to find the radius.
Solving for r, I get r = C/2π.
Plugging in 36 for C, I get r = 36/2π = 18/π.
The area of a circle is given by the formula A = πr^2.
Plugging in 18/π for r, I get A = π(18/π)^2 = 324/π.
This is the area of one circle, so I need to double it to get the sum of the areas of both circles.
The sum is 2(324/π) = 648/π square centimeters.