The sides of a square field are 12 meters. A sprinkler in the center of the field sprays a circular are with a diameter that corresponds to a side of the field. How much of the field is NOT reached by the sprinkler?

Question

Angus

Mathematics

23 October, 12:32

The sides of a square field are 12 meters. A sprinkler in the center of the field sprays a circular are with a diameter that corresponds to a side of the field. How much of the field is NOT reached by the sprinkler?

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Answers (1)

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Elise Little · Answer 1

Step-by-step explanation:

The formula for determining the area of a square is expressed as

Area = L²

Where

L represents length of each side of the square.

The side of the square is field us 12 meters long. Therefore

Area of the square field = 12² = 144ft²

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents radius if the circle.

π is a constant whose value is 3.14

Diameter of the circular area covered by the sprinkler is 12 meters.

Radius = 12/2 = 6 meters.

Area of the field covered by the sprinkler would be

Area = 3.14 * 6² = 113.04ft²

Therefore, the area of the field that is NOT reached by the sprinkler would be

144 - 113.04 = 30.96ft²