the radius of a circle when the numeric values of the circumference and the area are equal
PI r^2= 2PI r
r^2- 2r=0
(r-0)(r-2)=0
So what r values satisfy the equation. There are two.
so what is the answer
r=0 or r=2
The answer to the question is that the radius of the circle can be either 0 or 2.
To explain how we arrived at this answer, we started with the equation that relates the radius (r) to the circumference and the area of a circle. The equation is πr^2 = 2πr, where π is a mathematical constant approximately equal to 3.14159.
By rearranging the equation, we get r^2 - 2r = 0. This equation is a quadratic equation, where we want to find the values of r that make the equation true.
To solve this quadratic equation, we can factor it by finding two values that multiply together to give 0. In this case, we can factor the equation as (r - 0)(r - 2) = 0.
Since the product of two numbers is 0 if and only if one or both of the numbers is 0, we conclude that either (r - 0) = 0 or (r - 2) = 0.
Solving these two equations gives us r = 0 or r = 2. These are the two values of r that satisfy the equation.
Therefore, the answer is that the radius of the circle can be either 0 or 2.