Question

A sprinkler rotates 360 to water a circular region. If the total area watered is approximately 1121 yd^2 , determine the radius of the region (the radius is the length of the stream of water). Round the answer to the nearest yard.

Answer 1

To find the radius of a circular region watered by a sprinkler, use the formula for the area of a circle, A = πr^2, and solve for r. For an area of approximately 1121 yd^2, the radius is about 18.89 yd, which rounds to 19 yards.

Step-by-step explanation:

The student is asking how to determine the radius of a circular region watered by a sprinkler system, given the total area. The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius of the circle. The student has provided the total area as approximately 1121 yd2.

To find the radius, we can rearrange the area formula to solve for r:
r = √(A/π).

Plugging in the given area:

r = √(1121 yd2/π) ≈ √(356.85734 yd2) ≈ 18.89 yd.

Rounding to the nearest yard, the radius of the circular region is approximately 19 yards.