A circular flower bed is surrounded by a path 4m wide . the diameter of the flower bed is 66m . what is the area of this path

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427.2566

a circular flower bed is saraundid by a path 5miter wide the diameter of flower bed is 65miter what is the area of the path

7.852

To find the area of the path surrounding the circular flower bed, we need to subtract the area of the flower bed from the area of the larger circle formed by the outer edge of the path.

1. First, we need to find the radius of the flower bed. The diameter of the flower bed is given as 66m, so the radius (r) is half of the diameter: r = 66m / 2 = 33m.

2. Next, we need to find the radius of the larger circle formed by the outer edge of the path. Since the path is 4m wide, the radius of this larger circle will be the sum of the radius of the flower bed and the width of the path: R = 33m + 4m = 37m.

3. Now we can calculate the area of the flower bed using the formula A_flower_bed = π * r^2, where π is a constant approximately equal to 3.14159: A_flower_bed = 3.14159 * (33m)^2.

A_flower_bed = 3.14159 * (33m * 33m) = 3.14159 * 1089m^2 ≈ 3418.43883m^2.

4. Finally, we can find the area of the path by subtracting the area of the flower bed from the area of the larger circle: A_path = A_larger_circle - A_flower_bed.

A_path = π * R^2 - A_flower_bed = 3.14159 * (37m)^2 - 3418.43883m^2.

A_path = 3.14159 * 1369m^2 - 3418.43883m^2 ≈ 4289.41968m^2 - 3418.43883m^2.

A_path ≈ 870.98085m^2.

Therefore, the area of the path surrounding the circular flower bed is approximately 870.98085 square meters.