Final answer:
The area of the circular path inside a 20m diameter park, with a 1m wide path, is 19π square meters. This is determined by subtracting the area of the smaller circle (81π) from the larger circle (100π), revealing the specific region occupied by the path within the park's boundary.
Step-by-step explanation:
To find the area of the path, we need to subtract the area of the smaller circle (path) from the area of the larger circle (park). The area of the larger circle can be found using the formula A = πr², where r is the radius. Here, the diameter of the larger circle is 20m, so the radius is 10m. Therefore, the area of the larger circle is 100π square meters. Similarly, the area of the smaller circle (path) can be found using the same formula, but with a radius of 9m (radius of larger circle - width of the path). Therefore, the area of the smaller circle is 81π square meters. To find the area of the path, we subtract the area of the smaller circle from the area of the larger circle: Area of the path = Area of the larger circle - Area of smaller circle = 100π - 81π = 19π square meters.