Question

14 multiple choice 1 point a sector of a circle has a central angle measure of 310 degrees. if the radius of the circle is 2 feet, what is the area of the sector? 10.82 square feet 5.41 square feet 21.64 square feet 12.31 square feet

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 \(\theta = 310^{\circ}\) and \(r = 2\) feet.

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Step3: Calculate the numerical value

Using \(\pi\approx3.14\), we have \(A=\frac{31\times3.14}{9}=\frac{97.34}{9}\approx10.82\)

Answer:

10.82 square feet