Question

in circle q with ( mangle pqr = 86^{circ} ) and ( pq = 6 ), find the area of sector ( pqr ). round to the nearest hundredth.

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 in degrees and \(r\) is the radius of the circle.

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

Given that \(\theta = 86^{\circ}\) and \(r = PQ=6\).

Step3: Substitute the values into the formula

Substitute \(\theta = 86\) and \(r = 6\) into the formula \(A=\frac{\theta}{360}\times\pi r^{2}\).

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Step4: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(A=\frac{86\times3.14159}{10}\).

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Answer:

\(27.02\)