Question

a sector of a circle has a central angle of 150°. find the area of the sector if the radius of the circle is 17 cm. give your answer accurate to 2 decimal places. cm²

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: Substitute the given values into the formula

Here, \(\theta = 150^{\circ}\) and \(r = 17\space cm\).

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Step3: Calculate the numerical value

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Answer:

\(379.13\space cm^{2}\)