A circle has a circumference of 31.4 cm. What is its area?
["What’s the Area of a Circle with a Circumference of 31.4 cm?", "Understanding the relationship between a circle’s circumference and its area is essential in geometry—and this calculation is simpler than you might think. If you know a circle’s circumference, you can determine its radius, then use that to find the area. Here, we’ll explore how to solve for the area when the circumference is 31.4 cm.", "### Step 1: Understand the Formula for Circumference\nThe circumference ( C ) of a circle is given by the formula:", "[\nC = 2\pi r\n]\nwhere ( r ) is the radius.", "### Step 2: Solve for the Radius\nGiven ( C = 31.4 ) cm, we rearrange the formula to find ( r ):", "[\nr = \frac{C}{2\pi} = \frac{31.4}{2 \ imes 3.14} = \frac{31.4}{6.28} = 5 \ ext{ cm}\n]", "So, the radius of the circle is 5 cm.", "### Step 3: Use the Radius to Find the Area\nThe area ( A ) of a circle is calculated using:", "[\nA = \pi r^2\n]", "Substituting ( r = 5 ) cm:", "[\nA = \pi \ imes 5^2 = 25\pi\n]", "Using ( \pi \approx 3.14 ), the approximate area is:", "[\nA = 25 \ imes 3.14 = 78.5 \ ext{ cm}^2\n]", "### Final Answer\nA circle with a circumference of 31.4 cm has an area of 78.5 cm².", "### Why This Matters\nWhether you're designing a circular garden, calculating material needs in construction, or studying geometry, knowing how to convert circumference to area simplifies project planning and mathematical problem-solving. With just a few basic formulas, you can quickly uncover key properties of any circle.", "---", "Summary:\n- Circumference ( C = 31.4 ) cm\n- Radius ( r = 5 ) cm\n- Area ( A = \pi r^2 = 78.5 ) cm²", "Use this method anytime you need to find area from circumference—quick and accurate!"]
