Question

A water sprinkler has a range of 5 meters as shown. The jet of water from the sprinkler sweeps out at an angle of 85° as the nozzle turns. What is the area watered by the sprinkler? Use the value π = 3.14, and round your answer to one decimal place.

Answer 1

Take a look at the attachment below. It may help!

With this sector we can create a proportion to find the area watered by the sprinkler. 85 degrees over a total 360 degrees would be simplified to the following -

17 / 72 = ( About ) 4.235

Thus, we can calculate the area of the circle with a range of 5 meters radius, and divide by about 4.235 to receive the area watered by the sprinkler, or the area of the sector -

$Area( Full Circle ) = \pi r^2,\\Area( Full Circle ) = \pi * ( 5 )^2,\\Area( Full Circle ) = 25\pi,\\\\Area( Full Circle ) = ( About ) 78.5$

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$Area( Watered By Sprinkler ) / Area( Sector ) = 78.5 / 4.235,\\Area( Watered By Sprinkler ) / Area( Sector ) = ( About ) 18.5$

The solution should be about 18.5 meters^2