### 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 want to find the sum of the areas of the circles, so I need to know the radius of each circle.
The wire is cut into two equal pieces, so each piece is 72/2 = 36 cm long.
The piece of wire forms 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 C = 36, I get r = 36/(2π) = 18/π cm.
Now I can use the formula for the area of a circle, A = πr^2, to find the area of each circle.
Plugging in r = 18/π, I get A = π(18/π)^2 = (324/π) cm^2.
The sum of the areas of the two circles is then 2A = 2(324/π) = (648/π) cm^2.