A farmer uses a center-pivot irrigation system to water a large crop field
MATHEMATICS · Subjective · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles
Problem
A farmer uses a center-pivot irrigation system to water a large crop field. The irrigation system consists of a long boom of length 400 m that rotates around a central water source. Due to an adjacent straight highway intersecting the circular path, the system is programmed to only rotate through an angle of 285∘ before reversing its direction to avoid watering the road. Calculate the total length of the curved boundary path traced by the outer wheel of the irrigation boom and the area of the field that receives water. Provide a justification for the degree of accuracy in your measurements and evaluate whether your calculated area is a realistic expectation for an agricultural farm sector.