The sides of a square field are 24 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth. Use 3.14 for π.

Question

Mathematics

Cristofer Norton

22 May, 14:34

The sides of a square field are 24 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth. Use 3.14 for π.

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Answers (1)

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Johnny Burke · Answer 1

Step-by-step explanation:

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

Area = Length²

Length = 24 meters

Area = 24² = 576 m²

The formula for determining the circular area covered by the sprinkler is expressed as

Circular area = πr²

Where

r represents the radius

π = 3.14

From the information given,

Diameter = 24 meters

Radius = diameter/2 = 24/2 = 12 meters

Area = 3.14 * 12² = 452.16 m²

Therefore, the area of the field not reached by the sprinkler is

576 - 452.16 = 123.84 m²