To find the area of the circle given its circumference, we can follow a few straightforward steps. The formula for the circumference (C) of a circle is:
C = 2πr
where r is the radius of the circle. In this case, we know that:
5π = 2πr
Next, we can simplify this equation by dividing both sides by π, which gives us:
5 = 2r
Now, solve for r:
r = 5 / 2 = 2.5 cm
Now that we have the radius, we can find the area (A) of the circle using the area formula:
A = πr²
Substituting our value for r:
A = π(2.5)²
Calculating (2.5)² gives us:
(2.5)² = 6.25
So the area is:
A = π × 6.25
This means:
A = 6.25π cm²
Thus, the area of the circle is 6.25π cm².