Find the area of the sector to the nearest square root

Question

A sprinkler is designed to rotate 360 degrees clockwise, and then 360 degrees counterclockwise to water a circular region with a radius of 12 feet. The sprinkler is located in the middle of the circular region. It begins malfunctioning and is only able to rotate 330 degrees in each direction.

 

Answer 1

instructions "to the nearest square root" are poorly expressed!

Normally, we are asked either to find a numerical answer in exact form (meaning that a factor such as √3 remains in that form rather than using its approximation 1.732050808), OR we're asked to get a decimal approximation accurate to some number of decimal places.

As to the problem itself, you just need to figure out the sector's central angle (θ, for partial coverage); once you have done that, take θ/360 of the whole circle's area.