Question

a sector of a circle has a central angle of 135°. find the area of the sector if the radius of the circle is 11 cm. cm² question help: license 1 ancestorauthors otherattribution message instructor submit question

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

Given \(\theta = 135^{\circ}\) and \(r = 11\space cm\).

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Using \(\pi\approx3.14\), we have \(A=\frac{363\times3.14}{8}=\frac{1139.82}{8}=142.4775\)

Answer:

\(142.48\space cm^{2}\) (rounded to two decimal places)