An urban planner is designing a circular roundabout with a radius of 10 meters, surrounded by a circular path that is 2 meters wide. What is the area of the path alone in square meters?

["Understanding the Area of a Circular Roundabout with an Around-Path: A Practical Guide for Urban Planning", "When designing urban spaces, roundabouts have become popular for improving traffic flow and enhancing safety. A well-designed circular roundabout not only functions efficiently but can also integrate green spaces or pedestrian zones—like a circular path surrounding the central island. In this article, we explore how to calculate the area of such a surrounding path, using a real-world example: an urban roundabout with a central island of radius 10 meters and a 2-meter-wide circular path surrounding it. Whether you’re an urban planner, architect, or student, understanding these calculations ensures efficient and attractive public space design.", "---", "### The Urban Roundabout: A Simple Yet Effective Design", "Imagine a circular roundabout with a central circular island of radius 10 meters. A smooth, accessible path 2 meters wide surrounds this island, forming a concentric outer circle. To determine the area of just the path (not including the island), we calculate the difference between the area of the larger outer circle and the inner circular island.", "---", "### Step-by-Step Calculation of the Path’s Area", "1. Dimensions of the Roundabout\n- Radius of the central island (inner circle):\n [\n r_{\ ext{inner}} = 10 \ ext{ meters}\n ]", "- Width of the surrounding path:\n [\n w = 2 \ ext{ meters}\n ]", "- Radius of the outer edge (island plus path):\n [\n r_{\ ext{outer}} = r_{\ ext{inner}} + w = 10 + 2 = 12 \ ext{ meters}\n ]", "2. Area of the Full Circle (Including Path and Island)\nArea of a circle is given by the formula ( A = \pi r^2 ).\n[\nA_{\ ext{outer}} = \pi \ imes (12)^2 = \pi \ imes 144 = 144\pi \ ext{ square meters}\n]", "3. Area of the Central Island\n[\nA_{\ ext{inner}} = \pi \ imes (10)^2 = \pi \ imes 100 = 100\pi \ ext{ square meters}\n]", "4. Area of the Path Alone\nSubtract the inner area from the outer area:\n[\nA_{\ ext{path}} = A_{\ ext{outer}} - A_{\ ext{inner}} = 144\pi - 100\pi = 44\pi \ ext{ square meters}\n]", "5. Final Numerical Estimate\nUsing ( \pi \approx 3.1416 ),\n[\nA_{\ ext{path}} \approx 44 \ imes 3.1416 = 138.23 \ ext{ square meters}\n]", "---", "### Why This Matters in Urban Planning", "Calculating the area of surrounding features like pedestrian plazas or green edges around roundabouts helps planners:", "- Estimate construction costs for materials such as paving, vegetation, or surfacing.\n- Ensure adequate space for accessibility and landscaping.\n- Enhance the aesthetic and functional value of urban cores.", "Moreover, a 2-meter-wide path provides space for foot traffic, cyclists, and landscaping, transforming a utility feature into an enjoyable public amenity.", "---", "### Summary", "- Central island radius: 10 meters\n- Path width: 2 meters\n- Outer radius: 12 meters\n- Area of the path alone: ( 44\pi \approx 138.23 \ ext{ m}^2 )", "This calculation is essential for precise and sustainable urban design—proving that even the simplest roundabout can be a strategic element in creating livable cities.", "---", "Keywords: urban planner, circular roundabout area, circular path around island, roundabout design, urban planning calculation, area of circular path, sustainable city infrastructure, geometry in architecture, pedestrian space calculation.", "---", "By mastering these calculations, urban planners can design roundabouts that balance traffic efficiency with public space quality—making cities smarter and more beautiful, one meter at a time."]