Answer: 2 cm
Explanation:
We can set up an equation using the given formula for the circumference of a circle and the area of a circle to solve for the radius (r).
Given:
2πr = πr²
Move terms to one side:
0 = πr² - 2πr
πr² - 2πr = 0
Factor:
r(πr - 2π) = 0
Set factors equal to 0:
πr - 2π = 0 r = 0
Solve unsolved factor:
πr - 2π = 0
πr = 2π
r = 2
The radius cannot be 0, so the radius is 2.