How to Find the Area of a Circle with Circumference

To find the area of a circle when you have the circumference, you can follow these steps:

1. First, recall the formulas involved. The circumference (C) of a circle is given by the formula: C = 2πr, where r is the radius.
2. From the circumference, you can solve for the radius:
• r = C / (2π)
3. Once you have the radius, you can find the area (A) using the area formula for a circle: A = πr².
4. Substituting the expression for radius into the area formula, you get:
• A = π(C / (2π))²
5. This simplifies to:
• A = (C²) / (4π)

Now, you can easily calculate the area of the circle using just the circumference. For instance, if the circumference is 31.4 units:

• Calculate the area:
• A = (31.4²) / (4π) ≈ 78.5 square units

This method provides a straightforward way to find the area of a circle if you start with the circumference.