An urban planner is designing a new park with a circular pond. The pond has a diameter of 20 meters. A circular walking path is to be constructed around the pond, with a uniform width of 3 meters. What is the circumference of the outer edge of the walking path?
["Designing Sustainable Green Spaces: Calculating the Circumference of a Pond with a Walking Path", "Urban planners continually seek innovative ways to enhance green spaces in cities, balancing aesthetics, functionality, and environmental benefits. A recent design project exemplifies this mission: a circular pond integrated into a vibrant urban park, surrounded by a uniformly wide circular walking path. This article explores the key geometric principle behind the path’s dimensions and explains how to calculate its outer circumference — a vital detail for both planning and public enjoyment.", "### The Core Design: A Central Pond and a Relaxing Path", "At the heart of the park lies a serene 20-meter-diameter circular pond. To provide space for pedestrians and encourage sustainable recreation, a wide 3-meter path is to be built around it. This path extends uniformly outward, creating a smooth circular ring around the pond. Understanding the outer dimensions — particularly the circumference of the path’s outer edge — is essential for path construction, surface materials estimating, and lighting layout.", "### Step-by-Step Calculation: Diameter of the Outer Edge", "To find the circumference of the outer edge of the walking path, we begin with basic circle geometry.", "- Pond diameter: 20 meters\n- Width of the path: 3 meters", "Because the path surrounds the pond uniformly, the radius of the outer edge is the sum of the pond’s radius and the path’s width.", "1. Calculate the pond’s radius:\n [\n \ ext{Radius of pond} = \frac{20}{2} = 10 \ ext{ meters}\n ]", "2. Add the path width to get the outer radius:\n [\n \ ext{Outer radius} = 10 + 3 = 13 \ ext{ meters}\n ]", "3. Use the formula for circumference (C = 2\pi r):\n [\n C = 2 \pi (13) = 26\pi \ ext{ meters}\n ]", "### Final Circumference Value", "Using the approximation (\pi \approx 3.1416):\n[\n26\pi \approx 26 \ imes 3.1416 \approx 81.68 \ ext{ meters}\n]", "Thus, the circumference of the outer edge of the walking path is approximately 81.68 meters — a smooth, continuous path encircling the gentle curve of the pond.", "### Why This Matters for Urban Planning", "Beyond aesthetics, accurate geometric calculations ensure practical implementation. The path’s diameter influences material quantities, drainage design, and accessibility planning. Moreover, circular forms promote flow and visual harmony, inviting visitors to walk, relax, and connect with nature in the urban fabric.", "### Conclusion", "Designing urban green spaces requires precision and vision. By applying simple yet powerful geometric principles — such as calculating the circumference of a concentric circular path — planners ensure both functional and beautiful outcomes. The 13-meter radius outer edge of the walking path surrounding the 20-meter pond creates a circular journey of about 81.68 meters — a perfect loop for reflection, exercise, and community life within the city’s rhythm.", "---", "Keywords: urban park design, circular walking path, pond circumference, urban planner, sustainable city design, geometric calculation, public space planning, walking path circumference, circular park, eco-friendly urban development."]
