A circle has a circumference of 31.4 cm. Find the area of the circle in square centimeters.
["# How to Find the Area of a Circle When Given the Circumference", "Understanding how to calculate the area of a circle from its circumference is a fundamental skill in geometry. Whether you're a student, teacher, or math enthusiast, knowing how to convert between these two key circle measurements is incredibly useful. In this article, we’ll explore how to determine the area of a circle with a circumference of 31.4 cm, step by step.", "## The Relationship Between Circumference and Radius", "The circumference ( C ) of a circle is calculated using the formula:", "[\nC = 2\pi r\n]\nwhere ( r ) is the radius of the circle and ( \pi ) (pi) is approximately 3.14.", "Given the circumference is 31.4 cm, we plug this value into the formula:", "[\n31.4 = 2\pi r\n]", "To solve for the radius ( r ), divide both sides by ( 2\pi ):", "[\nr = \frac{31.4}{2\pi}\n]", "Using ( \pi \approx 3.14 ):", "[\nr = \frac{31.4}{2 \ imes 3.14} = \frac{31.4}{6.28} = 5 \ ext{ cm}\n]", "So, the radius of the circle is 5 centimeters.", "## Finding the Area from the Radius", "Once you have the radius, finding the area ( A ) of the circle is straightforward using the formula:", "[\nA = \pi r^2\n]", "Substituting ( r = 5 ) cm:", "[\nA = \pi (5)^2 = \pi \ imes 25 = 25\pi \ ext{ cm}^2\n]", "Using ( \pi \approx 3.14 ), the numerical value is:", "[\nA \approx 25 \ imes 3.14 = 78.5 \ ext{ cm}^2\n]", "## Final Answer", "The area of a circle with a circumference of 31.4 cm is exactly:", "[\n\boxed{25\pi \ ext{ cm}^2} \quad \ ext{(approximately } 78.5 \ ext{ cm}^2\ ext{)}\n]", "This means not only is the radius 5 cm, but the total space enclosed within the circle is 25π square centimeters—perfect for calculations in geometry, science, or everyday applications.", "Whether you're solving algebra problems, designing products, or studying for exams, mastering this conversion helps strengthen your grasp of circular relationships in math. Remember, knowing how circumference connects to area makes it easier to tackle real-world problems involving circles!"]
