A circular garden has a diameter of 14 meters. If a path 1 meter wide is built around the garden, what is the area of the path alone?
["Understanding the Area of a Circular Garden with a 1-Meter Walking Path", "When designing beautiful outdoor spaces, one popular choice is a circular garden — elegant, space-efficient, and highly sustainable. In this SEO-optimized article, we explore a practical example: a circular garden with a diameter of 14 meters, enhanced by a 1-meter-wide walking path surrounding it. Discover how to calculate the area of the path alone — a key factor for planning, landscaping, and maximizing functionality.", "### The Garden’s Basic Dimensions", "The garden is circular with a diameter of 14 meters, which means the radius is:", "[\nr = \frac{14}{2} = 7 \ ext{ meters}\n]", "### Adding the Path: Updated Layout", "A 1-meter-wide path surrounds the garden, increasing the total radius to:", "[\nR = 7 + 1 = 8 \ ext{ meters}\n]", "The circular space now includes both the garden and the path, forming a total area of radius 8 meters.", "### Step-by-Step: Calculating the Area of the Path", "To determine the area of just the path, follow these simple steps:", "1. Calculate the area of the larger circle (garden + path):\n [\n A_{\ ext{outer}} = \pi R^2 = \pi (8)^2 = 64\pi \ ext{ square meters}\n ]", "2. Calculate the area of the inner circle (pure garden):\n [\n A_{\ ext{inner}} = \pi r^2 = \pi (7)^2 = 49\pi \ ext{ square meters}\n ]", "3. Subtract to find the path’s area:\n [\n A_{\ ext{path}} = A_{\ ext{outer}} - A_{\ ext{inner}} = 64\pi - 49\pi = 15\pi \ ext{ square meters}\n ]", "### Final Result", "Using the approximation (\pi \approx 3.1416), the path’s area is approximately:", "[\nA_{\ ext{path}} \approx 15 \ imes 3.1416 = 47.12 \ ext{ square meters}\n]", "### Why This Matters for Garden Designers and Homeowners", "- Precise planning: Knowing the exact path area helps with material estimates and construction budgets.\n- Space optimization: Circular gardens with paths offer elegant layouts that enhance accessibility and aesthetics.\n- Functional distinction: Identifying the path area enables correct irrigation, planting zones, and safe walkway design.", "In summary, for a circular garden with a 14-meter diameter plus a 1-meter-wide surrounding path, the path area is (\mathbf{15\pi) square meters (about 47.12 m²) — a valuable insight for creating beautifully functional landscapes.", "---", "Keywords: circular garden area, path area calculation, circular garden with path, outer and inner circle area, landscaping calculations, home garden design, garden perimeter analysis"]
