A circle has a radius of 7 cm. Calculate the area of the circle and then find the circumference. What is the sum of the area and circumference? Use \(\pi \approx 3.14\).
["Circle Basics: Calculating Area and Circumference with Radius 7 cm", "A circle is a fundamental shape in geometry defined by a set of points equidistant from a central point, known as the center. The distance from the center to any point on the circle is called the radius—a key measurement we will use to find both the area and circumference of the circle.", "In this article, we’ll explore how to calculate the area and circumference of a circle with a radius of 7 cm, using the constant (\pi \approx 3.14). Then, we’ll add these two values to discover the total sum—providing a complete picture of how these two fundamental measurements relate.", "---", "### Given:\nRadius (r) = 7 cm\nApproximated value of (\pi \approx 3.14)", "---", "### Step 1: Calculate the Area of the Circle", "The formula for the area (A) of a circle is:\n[\nA = \pi r^2\n]", "Substituting (r = 7) cm and (\pi = 3.14):\n[\nA = 3.14 \ imes (7)^2 = 3.14 \ imes 49 = 153.86 \ ext{ cm}^2\n]", "So, the area is 153.86 cm².", "---", "### Step 2: Calculate the Circumference", "The circumference (C) of a circle is found using:\n[\nC = 2\pi r\n]", "Using (r = 7) cm and (\pi = 3.14):\n[\nC = 2 \ imes 3.14 \ imes 7 = 43.96 \ ext{ cm}\n]", "So, the circumference is 43.96 cm.", "---", "### Step 3: Find the Sum of the Area and Circumference", "Now, add the area and circumference:\n[\n\ ext{Sum} = \ ext{Area} + \ ext{Circumference} = 153.86 + 43.96 = 197.82 \ ext{ cm}\n]", "Thus, the total sum is 197.82 square centimeters and centimeters—a combined measure of space and perimeter for the circle.", "---", "### Summary\nFor a circle with a radius of 7 cm:\n- Area = 153.86 cm²\n- Circumference = 43.96 cm\n- Sum = 197.82", "Understanding these basic calculations helps in architecture, engineering, design, and everyday problem-solving involving circular shapes. Use (\pi \approx 3.14) for quick approximations or exact values when needed.", "---", "Key Takeaway:\nCombining area and circumference gives important spatial insight into a circle—ideal for real-world applications such as calculating material needs, designing round structures, or analyzing circular components.", "Let me know if you'd like a more advanced breakdown including exact (\pi) results or visual diagrams!"]
