Question

circle n has a radius of 6 inches. what is the area of the shaded sector? write an exact, simplified answer. square inches

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle of the sector and \(r\) is the radius of the circle.

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

From the problem, the radius \(r = 6\) inches and the central angle \(\theta=80^{\circ}\).

Step3: Substitute the values into the formula

Substitute \(r = 6\) and \(\theta = 80\) into \(A=\frac{\theta}{360}\times\pi r^{2}\).

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Step4: Simplify the expression

$$
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$$

Answer:

\(8\pi\) square inches