Question

question 2/a garden sprinkler sits on the ground, shooting water a distance of 22 feet and rotating, therebywatering part of the area inside a circle.suppose the sprinkler has rotated through an angle of 2.3 radians. what area (in feet²) of the lawnhas the water covered? give your answer as a decimal number.answer: ft²enter your answer as an integer or decimal number. examples: 3, -4, 5.5172enter dne for does not exist, oo for infinityquestion help: message instructor

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{1}{2}r^{2}\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step2: Identify the values of \(r\) and \(\theta\)

Given that the radius \(r = 22\) feet and the central angle \(\theta=2.3\) radians.

Step3: Substitute the values into the formula

Substitute \(r = 22\) and \(\theta = 2.3\) into \(A=\frac{1}{2}r^{2}\theta\).

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Step4: Calculate the result

\(242\times2.3=556.6\)

Answer:

\(556.6\)