A circular field is surrounded by a path of uniform width 2.5 m. The total area of the field, including the path, is 1078.125 m². If the area of the circular field (excluding the path) is 803.25 m², find the radius of the circular field and the radius including the path. (Use π ≈ 3.1416)
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Correct answer: B
Explanation
Given:
Width of path = 2.5 meters
Area including path = 1078.125 m²
Area of field (excluding path) = 803.25 m²
By formula:
Area of circle = πr²
Area of field
πr² = 803.25
3.1416 r² = 803.25
r² = 803.25 / 3.1416
r² = 255.67
r = 15.99 meters
Radius including path
R = r + 2.5 = 15.99 + 2.5 = 18.49 meters
Radius of field = 15.99 meters
Radius including path = 18.49 meters