### 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: To find the area of a circle, I need to know its radius.
I can use the formula C = 2πr, where C is the circumference and r is the radius, to find the radius of each circle.
Since I cut the wire into two equal pieces, each piece has a length of 72/2 = 36 cm.
So the circumference of each circle is 36 cm.
Plugging this into the formula, I get 36 = 2πr, which implies r = 18/π.
Now I can use the formula A = πr^2, where A is the area, to find the area of each circle.
Plugging in r = 18/π, I get A = π(18/π)^2, which simplifies to A = 324/π.
This is the area of one circle, so the sum of the areas of both circles is twice that, or 648/π.