What is the area of a circle with a circumference of 2π^2 square meters?
A = (pi)r^2
C = 2(pi)r
I'm sorry I don't understand how to incorporate those equations into finding the answer
first off, the circumference is measured in meters, not m^2.
If C = 2π^2, then
2πr = 2π^2
r = π
So, A = πr^2 = π^3 m^2
If you meant to find the circumference when the area is 2π^2 m^2,
πr^2 = 2π^2
r^2 = 2π
r = √2π
C = 2πr = 2π√2π = (2π)^(3/2)
Actually, I think you just messed up the whole question.
To find the area of a circle, you need to use the formula:
Area = π * radius^2
In this case, we are given the circumference, which is related to the radius by the formula:
Circumference = 2 * π * radius
Since the circumference in this case is 2π^2 square meters, we can set up the equation:
2π^2 = 2 * π * radius
To solve for the radius, we can divide both sides of the equation by 2π:
2π^2 / (2π) = radius
Simplifying, we get:
π = radius
Now that we have the radius, we can substitute it into the formula for the area of a circle:
Area = π * radius^2
Substituting π for the radius, we get:
Area = π * (π)^2
Simplifying further, we have:
Area = π * π^2
Considering that π^2 is a constant, we can compute it as π × π = π^2. So the final equation becomes:
Area = π^3
Therefore, the area of the circle with a circumference of 2π^2 square meters is π^3 square units.