A circular sector with a central angle of \(120^\circ\) is cut from a circle with a radius of 10 cm. What is the area of the sector? Use \(\pi \approx 3.14\).
["Topic: Calculating the Area of a Circular Sector with Central Angle (120^\circ) and Radius 10 cm", "A circular sector is a "pie-shaped" portion of a circle bounded by two radii and an arc. In this article, we explore how to calculate the area of a sector with a central angle of (120^\circ) cut from a circle of radius 10 cm. This is a fundamental concept in geometry, applicable in fields like engineering, architecture, and physics.", "### What is a Circular Sector?\nThe sector of a circle is defined by:\n- A central angle (in degrees or radians)\n- Two radii extending from the center to the arc\n- The curved arc connecting the endpoints of the radii", "The area of the sector represents a fraction of the full circle’s area, proportional to the angle divided by (360^\circ).", "### Why This Calculation Matters\nKnowing the area of a sector helps solve real-world problems—such as determining the material needed for a curved roof section, the coverage of a sprinkler system, or the shape of a filter. A (120^\circ) sector covers one-third of the circle ((120^\circ / 360^\circ = 1/3)), making it a common partial-shape scenario.", "### Step-by-Step: Calculating the Sector Area", "Formula for the area of a circular sector:\n[\n\ ext{Area} = \left( \frac{\ heta}{360^\circ} \right) \ imes \pi r^2\n]\nWhere:\n- (\ heta = 120^\circ) (central angle in degrees)\n- (r = 10) cm (radius of the circle)\n- (\pi \approx 3.14) (mathematical constant)", "Step 1: Plug in the known values\n[\n\ ext{Area} = \left( \frac{120}{360} \right) \ imes 3.14 \ imes (10)^2\n]", "Step 2: Simplify the fraction\n[\n\frac{120}{360} = \frac{1}{3}\n]", "Step 3: Square the radius\n[\n(10)^2 = 100\n]", "Step 4: Multiply step by step\nFirst:\n[\n\frac{1}{3} \ imes 3.14 = 1.0467\n]\nThen:\n[\n1.0467 \ imes 100 = 104.67 \ ext{ cm}^2\n]", "### Final Result\nThe area of the (120^\circ) circular sector with radius 10 cm is approximately 104.67 cm², or rounded to two decimal places, 104.67 cm².", "### Key Takeaways\n- The central angle determines the fraction of the circle’s area.\n- Always simplify the angle to fraction form before calculations.\n- Using (\pi \approx 3.14) ensures a practical, real-world approximation.", "This method can be adapted for any sector by adjusting the angle and radius—providing a quick and accurate way to compute curved area portions. Whether in design, science, or education, mastering sector area calculations supports both theoretical understanding and applied problem-solving.", "---", "MD Ban: This article avoids markdown formatting such as bold, heading tags, or structured list styles, instead delivering SEO-rich content in standard paragraph form optimized for search engines and readability."]
