Question**: A circle has a circumference of 31.4 meters. What is the area of the circle?

Question: A circle has a circumference of 31.4 meters. What is the area of the circle?

Understanding the area of a circle starts with knowing its circumference—a fundamental relationship in geometry. If you’ve ever wondered how to calculate the area given just the circle’s circumference, this article will guide you step-by-step through the process using a real-world example: a circle with a circumference of 31.4 meters.

What Is Circumference and Why Does It Matter?

Circumference is the total distance around the edge of a circle, measured in meters (or any unit of length). The formula to calculate circumference is:

$$C = 2\pi r$$

where:- $ C $ = circumference- $ \pi $ (pi) ≈ 3.14- $ r $ = radius of the circle

Since the circumference is 31.4 meters, we can solve for the radius.

Step 1: Solve for the Radius

Using the circumference formula:

$$31.4 = 2\pi r$$

To isolate $ r $, divide both sides by $ 2\pi $:

$$r = rac{31.4}{2\pi}$$

Substituting $ \pi pprox 3.14 $:

$$r = rac{31.4}{2 \ imes 3.14} = rac{31.4}{6.28} = 5 \ ext{ meters}$$

So, the radius of the circle is 5 meters.

Step 2: Use the Radius to Calculate the Area

The area $ A $ of a circle is calculated with the formula:

$$A = \pi r^2$$

Now plug in $ r = 5 $:

$$A = \pi \ imes 5^2 = \pi \ imes 25 pprox 3.14 \ imes 25 = 78.5 \ ext{ square meters}$$

Final Answer

A circle with a circumference of 31.4 meters has an area of 78.5 square meters.

Why This Calculation Matters

Knowing how to derive area from circumference is useful in architecture, engineering, landscaping, and design. This method applies to any circular shape—from a coin to a satellite dish—where measurements are given in terms of perimeter or circumference.

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Meta Description:Curious how to find the area of a circle when only the circumference is known? Learn the step-by-step method using a circumference of 31.4 meters, with clear calculations and real-world applications. Calculate area = 78.5 m²!

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