To find the area of a circle when its circumference is given, we’ll use the formulas for circumference and area. The circumference (C) of a circle is calculated using the formula:
C = 2πr
where r is the radius of the circle.
Given that the circumference is 8π meters, we can set up the equation:
8π = 2πr
To solve for r, divide both sides of the equation by 2π:
r = (8π) / (2π) = 4 meters
Now that we have the radius, we can calculate the area (A) of the circle using the formula:
A = πr²
Substituting the radius we found:
A = π(4)² = π(16) = 16π square meters
Therefore, the area of the circle whose circumference is 8π meters is 16π square meters.