#### 11520Question: An ancient circular mosaic has a radius of $12$ meters. A maintenance path of width $2$ meters is constructed around it. What is the area of the path?
["#### 11520Question: An ancient circular mosaic has a radius of $12$ meters. A maintenance path of width $2$ meters is constructed around it. What is the area of the path? \nCurious visitors and cultural enthusiasts are increasingly exploring historic sites like Roman villas or Byzantine courtyards where circular mosaics serve as centerpieces. As preservation projects expand across the U.S. — from private estates to museum grounds — attention grows on how functional access paths integrate with ancient beauty. This mix of heritage and practical design has spotlighted a precise geometric calculation: determining the area of a surrounding path around a circular mosaic.", "#### Why This Problem Matters Now \nIn sustainable heritage management, thoughtful path design balances visitor access with protection of delicate surfaces. The addition of a 2-meter-wide path around a 12-meter-radius mosaic isn’t just a maintenance detail — it reflects broader trends in cultural landscape planning. People search for smarter, more respectful ways to engage with history, and understanding the math behind such spaces deepens appreciation for preservation efforts. With millions exploring historic sites online, clear, accurate data supports both academic curiosity and informed decision-making.", "#### How to Calculate the Area of the Path \nThe path surrounds the mosaic like a protective ring, expanding outward uniformly. To find its area, calculate the difference between the outer circle’s area and the mosaic’s original area — a clear application of concentric circle geometry.", "First, compute the full radius including the path: \nRadius of mosaic = $12$ meters \nPath width = $2$ meters \nTotal radius = $12 + 2 = 14$ meters", "Now calculate: \n- Area of full circle (mosaic + path) = $\pi \ imes (14)^2 = 196\pi$ \n- Area of mosaic alone = $\pi \ imes (12)^2 = 144\pi$", "Subtracting yields the path’s area: \n$196\pi - 144\pi = 52\pi$ square meters", "This precise figure reflects how geometric precision supports planning for physical preservation, resonating with professionals and enthusiasts alike.", "#### Common Questions People Ask \nQ: Why isn’t the path measured simply as a ring’s outer circle area? \nA: Because the path is a strip between two circles —"]
