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The sides of a square field are 14 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

Respuesta :

To obtain the area that is not sprinkled, subtract the area of the circle from the area of the square field.

[tex]A=A_S-A_C[/tex]

Solve for the area of the square. Substitute the value of the sides into the equation.

[tex]\begin{gathered} A_S=s^2 \\ A_S=14^2 \\ A_S=196 \end{gathered}[/tex]

Solve for the area of the circle. Substitute the value of the radius into the equation. Note that the measure of the radius is half of the measure of the diameter. Since the diameter is 14 meters, the radius is 7 meters.

[tex]\begin{gathered} A_C=\pi r^2 \\ A_C=3.14(7^2) \\ A_C=3.14(49) \\ A_C\approx153.86 \end{gathered}[/tex]

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