There are \(\boxed{75}\) positive 3-digit numbers divisible by 12.**Question:** A wildlife habitat restoration specialist is designing a circular garden to support local biodiversity. The garden is to be inscribed in a square region with a side length of 10 meters. What is the area of the circular garden?

["The Surprising Link Between Math and Nature: A Circular Garden in a Square Garden Space", "When restoring wildlife habitats, every square meter and geometric precision counts—especially when designing natural spaces like circular gardens within defined boundaries. Imagine a square region measuring 10 meters on each side, perfectly suited for a beautifully inscribed circular garden that supports local biodiversity. But beyond aesthetics, such a design holds mathematical elegance and practical efficiency.", "A key geometric fact emerges: There are exactly (\boxed{75}) positive three-digit numbers divisible by 12. Understanding this number isn’t just a trivia point—it helps in planning modular planting zones, spacing features evenly, or dividing areas into quantifiable units for ecological studies. Let’s unpack how this percentage of three-digit count relates to efficient design planning in natural spaces.", "### Why the Number 75 Matters", "Three-digit numbers range from 100 to 999—totaling 900 numbers. Divisibility by 12 means a number must be divisible by both 3 and 4. The result of 75 such numbers shows there’s a structured, predictable distribution, helping designers divide spaces into manageable, evenly divisible units—crucial when creating microhabitats within a circular garden.", "### The Circular Garden Inspired by a Square", "Now, consider the wildlife habitat restoration project: a circular garden perfectly inscribed in a 10-meter square. This means the circle’s diameter equals the square’s side—10 meters—and its radius is 5 meters.", "Calculating the area of the circular garden:", "[\n\ ext{Area} = \pi r^2 = \pi \ imes 5^2 = 25\pi \ ext{ square meters}\n]", "Using (\pi \approx 3.1416),", "[\n25 \ imes 3.1416 = 78.54 \ ext{ square meters (approximately)}\n]", "This area provides sufficient space for native plants, insects, and small nesting sites—key for supporting biodiversity.", "### Practical Benefits", "- Efficient use of space: The circular shape minimizes perimeter waste and surrounds a uniform, accessible area.\n- Balanced design: 75 divisible by 12 points reflect patterns that can guide planting zones or observation paths evenly distributed across the garden.\n- Eco-friendly computation: Selecting numbers like 75 helps planners divide large plots into equal, sustainable units, aligning math with ecology.", "### Conclusion", "Geometry and ecology blend seamlessly in restoration projects. From the mathematical certainty of (\boxed{75}) three-digit numbers divisible by 12—symbolizing order and balance—to the careful circular garden inscribed in a square meter, both highlight how precision shapes thriving natural spaces. For wildlife habitats, such thoughtful design doesn’t just protect nature—it celebrates it with smart, measurable care.", "---", "🌿 Whether you're calculating circular areas or planning ecosystems, math helps restore — and nature rewards with life."]