Answer: 3544.90393 square meters
Step-by-step explanation: To find the area of the path surrounding the circular field, we need to subtract the area of the circular field from the area of the larger circle that includes the path.
The radius of the circular field is given as 77 m. The radius of the larger circle, which includes the path, is the sum of the radius of the circular field and the width of the path.
Radius of larger circle = 77 m + 7 m = 84 m
The area of the circular field is given by the formula:
Area of circular field = π * (radius of circular field)^2
Area of circular field = π * (77 m)^2
The area of the larger circle is given by the formula:
Area of larger circle = π * (radius of larger circle)^2
Area of larger circle = π * (84 m)^2
The area of the path surrounding the circular field is then given by:
Area of path = Area of larger circle - Area of circular field
Area of path = π * (84 m)^2 - π * (77 m)^2
Area of path = π * (84^2 - 77^2) m^2
Using the values of π = 3.14159, 84^2 = 7056, and 77^2 = 5929, we can calculate the area of the path.
Area of path = 3.14159 * (7056 - 5929) m^2
Area of path ≈ 3.14159 * 1127 m^2
Area of path ≈ 3544.90393 m^2
Therefore, the area of the path surrounding the circular field is approximately 3544.90393 square meters.