A sprinkler is designed to rotate 360∘ clockwise, and then 360∘ counterclockwise to water a circular region with a radius of 12 feet. the sprinkler is located in the middle of the circular region. the sprinkler begins malfunctioning and is only able to rotate 330∘ in each direction. find the area of the sector to the nearest square foot.

Question

Harold Brennan

Mathematics

5 October, 15:02

A sprinkler is designed to rotate 360∘ clockwise, and then 360∘ counterclockwise to water a circular region with a radius of 12 feet. the sprinkler is located in the middle of the circular region. the sprinkler begins malfunctioning and is only able to rotate 330∘ in each direction. find the area of the sector to the nearest square foot.

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Kaydence Weiss · Answer 1

The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and 360° (whereas the area of the sector is proportional to its angle, and 360° is the angle for the whole circle):

The area of the sector = πr²·Θ/360

=3.14 x 12² x 330 : 360 ≈ 415 ft²