#### 8.66Question: A circular garden has a radius of $ r $ meters. A path of width $ w $ meters is constructed around the garden. What is the area of the path in terms of $ r $ and $ w $?
["#### 8.66Question: A circular garden has a radius of $ r $ meters. A path of width $ w $ meters is constructed around the garden. What is the area of the path in terms of $ r $ and $ w $?", "Why’s this question gaining attention in the US right now? Smart homeowners and landscapers are rethinking outdoor space efficiency and aesthetic appeal. With rising interest in sustainable yard design and smart outdoor living, hidden geometries like garden paths are emerging as both functional and visually striking elements. Models and gardeners alike are exploring how circular features, combined with surrounding clear edge space, transform garden functionality—blending nature with structured design.", "When calculating the area of a path surrounding a circular garden, think of it as the difference between two concentric circles. The garden itself has radius $ r $, and the full layout—garden plus path—extends outward by $ w $ meters. The outer circle therefore has radius $ r + w $. The area of this full circle is $ \pi(r + w)^2 $. Subtracting the garden’s area, $ \pi r^2 $, reveals the path’s area.", "Mathematically, the area of the path is \n$$ \n\ ext{Path Area} = \pi(r + w)^2 - \pi r^2 \n= \pi[(r + w)^2 - r^"]
