Based on the given information, the radius of the circular field is approximately 140 m.
How to find the radius of the circular field
To find the radius of the circular field, calculate the diameter of the circle and then divide it by 2 to obtain the radius.
Given:
Length of the tank = 180 m
Breadth of the tank = 120 m
Area of the land portion of the field = 40000 m²
To find the diameter of the circular field, subtract the area of the tank from the total area of the land portion:
Area of the tank = Length × Breadth = 180 m × 120 m = 21600 m²
Area of the circular field = Area of the land portion + Area of the tank
= 40000 m² + 21600 m²
= 61600 m²
Now, the area of a circle is given by the formula:
Area of a circle = π × radius²
Rearranging the formula to solve for the radius:
radius = √(Area of the circular field / π)
Plugging in the values:
radius = √(61600 m² / π)
Calculating the value:
radius ≈ √(19614.232 m²)
≈ 140.05 m
Therefore, the radius of the circular field is approximately 140 m.