Question

A farm uses an irrigation system to water crops in a circular pattern. The rotating arm is 100 meters in length. As the arm rotates through an angle of π/2 radians, it forms a circular arc. What is the length, in meters, of the arc?

A. 50 meters
B. 50π meters
C. 200 meters
D. 200π meters

Answer 1

The length of the arc is found using the formula: Arc Length = (Angle in radians) × (Radius). For an angle of π/2 radians and a radius of 100 meters, the arc length is 50π meters. The correct answer is Option B: 50π meters.

Step-by-step explanation:

To calculate the length of the arc created by the rotating irrigation arm, we will use the formula for arc length given an angle in radians, which is:

Arc Length = (Angle in radians) × (Radius of the circle)

The angle through which the arm rotates is π/2 radians, and the radius of the circular pattern created by the arm is 100 meters. Using the formula, we can calculate the arc length as follows:

Arc Length = π/2 × 100 meters

Arc Length = 50π meters

Therefore, the correct answer for the length of the arc is Option B: 50π meters.