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A center-pivot or circle sprinkler is used on large farms to irrigate crops. The sprinkler rotates an irrigation arm 360^(@) from a fixed center. The outside of the irrigation arm travels 3,140 yards with each rotation. Determine the length of the irrigation arm in yards.

55. A center-pivot or circle sprinkler is used on large farms to irrigate crops. The sprinkler rotates an irrigation arm 360∘ 360^{\circ} from a fixed center. The outside of the irrigation arm travels 33,140140 yards with each rotation. Determine the length of the irrigation arm in yards.

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Full solution

Q. 55. A center-pivot or circle sprinkler is used on large farms to irrigate crops. The sprinkler rotates an irrigation arm 360∘ 360^{\circ} from a fixed center. The outside of the irrigation arm travels 33,140140 yards with each rotation. Determine the length of the irrigation arm in yards.
  1. Calculate Circumference: Calculate the circumference of the circle made by the irrigation arm.\newlineCircumference formula: C=2⋅π⋅rC = 2 \cdot \pi \cdot r\newlineGiven C=3,140C = 3,140 yards
  2. Solve for Radius: Rearrange the formula to solve for the radius (length of the irrigation arm).\newliner=C2πr = \frac{C}{2 \pi}\newliner=3,1402πr = \frac{3,140}{2 \pi}
  3. Calculate Radius: Use the value of pi as approximately 3.143.14 to calculate the radius.\newliner=3,1402×3.14r = \frac{3,140}{2 \times 3.14}\newliner=3,1406.28r = \frac{3,140}{6.28}
  4. Find Radius: Perform the division to find the radius.\newliner=500r = 500 yards

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