A circle has a circumference of 31.4 cm. What is its area? (Use \( \pi \approx 3.14 \))
["Calculating the Area of a Circle: Using Circumference of 31.4 cm", "Understanding the relationship between a circle’s circumference and area is a fundamental concept in geometry. Whether you're solving a math problem or applying it in real-world scenarios, knowing how to find the area from the circumference can be incredibly useful. In this article, we’ll explore how to calculate the area of a circle when given its circumference—specifically, when the circumference is 31.4 cm and using ( \pi \approx 3.14 ).", "### What Is Circumference and Why Does It Matter?", "The circumference of a circle is the total distance around its edge. It is directly related to the circle’s diameter through the formula:", "[\nC = \pi \ imes d\n]", "where ( C ) = circumference, ( d ) = diameter, and ( \pi ) is approximately 3.14.", "Once you know the circumference, you can find the diameter by rearranging the formula:", "[\nd = \frac{C}{\pi}\n]", "This diameter then lets us calculate the radius—since radius ( r = \frac{d}{2} )—which is essential for finding the area.", "### Step-by-Step: Find the Area from Circumference 31.4 cm", "Given:\n- Circumference ( C = 31.4 , \ ext{cm} )\n- Approximation: ( \pi \approx 3.14 )", "Step 1: Find the diameter", "[\nd = \frac{C}{\pi} = \frac{31.4}{3.14} = 10 , \ ext{cm}\n]", "Step 2: Find the radius", "[\nr = \frac{d}{2} = \frac{10}{2} = 5 , \ ext{cm}\n]", "Step 3: Use the area formula", "The area ( A ) of a circle is given by:", "[\nA = \pi r^2\n]", "Substituting ( r = 5 , \ ext{cm} ) and ( \pi \approx 3.14 ):", "[\nA = 3.14 \ imes (5)^2 = 3.14 \ imes 25 = 78.5 , \ ext{cm}^2\n]", "### Final Answer", "A circle with a circumference of 31.4 cm has an area of 78.5 cm² when using ( \pi \approx 3.14 ).", "### Practical Applications", "Knowing how to calculate area from circumference is useful in design, construction, or everyday life—such as figuring out the material needed to cover a circular garden, the area a wheel occupies, or the surface area of a bowl. A clean, accurate calculation ensures efficiency and precision in both academic and practical settings.", "---", "Summary:\n- Circumference = 31.4 cm\n- ( \pi \approx 3.14 )\n- Radius = 5 cm\n- Area = 78.5 cm²", "By using these formulas step by step, solving for the area becomes straightforward—turning a simple circumference into a full geometric understanding."]
