a lawn sprinkler located at the corner of a yard is set to rotate through 90 degrees and project 30.0 feet. what area of lawn is watered by the sprinkler? round to the nearest whole

Answer :

elcharly64

Answer:

[tex]A\approx 707 \ ft^2[/tex]

Step-by-step explanation:

Area of a circular sector

A circular sector is defined by a central angle θ and the radius of the circle r. The area of the circular sector is:

[tex]{\displaystyle A={\frac {r^{2}\theta }{2}}}[/tex]

Note: θ must be expressed in radians.

The lawn sprinkler rotates θ=90° to an area of radius r=30 feet.

Expressing θ in radians:

[tex]\theta=90*\pi/180=\pi/2[/tex]

The area is:

[tex]{\displaystyle A={\frac {30^{2}\pi/2 }{2}}}[/tex]

[tex]A=706.9\ ft^2[/tex]

[tex]\boxed{A\approx 707 \ ft^2}[/tex]

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