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There are two sprinklers that spread water in a circular sector (90 degrees). They only spray in an 18-foot radius. (See the diagram:

One sprinkler is in the top left corner and the other is in the bottom right corner. Part of the lawn is not covered by either sprinkler.)
The lawn measures 18° by 36, and each sprinkler has a spray radius of 18%
What is the area of the section of lawn that is not watered by either sprinkler?

1 Answer

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The area of the section of the lawn that is not watered by either sprinkler is 139.06 feet².

How do we find the area not watered by the sprinkler?

The lawn measures 18' by 36', the total area is:

Total area = 18 × 36

Total area = 648

Each sprinkler covers a quarter circle with a radius of 18 feet because they only spray in a 90-degree (or quarter) sector.

The area of a full circle is πr², so the area covered by each sprinkler is a quarter of that:

Area covered by one sprinkler = πr²/4

Area_not watered = Area_lawn − 2 ×( 1/4πr²)

Area_not watered = 648 − 2 ×( 1/4πr²)

(1/4)π(324) = 254.469

2 × 254.469 = 508.938

Area_not watered = 648 - 508.938

Area_not watered = 139.062

The area of the section of the lawn that is not watered by either sprinkler is approximately 139.06 square feet.

There are two sprinklers that spread water in a circular sector (90 degrees). They-example-1
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