To find the area of a circle when the circumference is given, we can start by using the formula for the circumference of a circle:
C = 2πr
where C is the circumference and r is the radius of the circle. Given that the circumference is 8π m, we can set up the equation:
8π = 2πr
Now, we can divide both sides by 2π to solve for r:
r = 8π / 2π = 4 m
Now that we have the radius, we can use it to find the area of the circle using the area formula:
A = πr²
Substituting the radius we found:
A = π(4 m)² = π(16 m²) = 16π m²
Thus, the area of the circle whose circumference is 8π m is 16π m².