Question

1. find the area of the sector.

24.7 in²
13 in²
10.8 in²
37.7 in²

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle with radius \( r \) and central angle \( \theta \) (in degrees) is \( A=\frac{\theta}{360}\times\pi r^{2} \). Here, the radius \( r = 6\) inches and the central angle \( \theta=120^{\circ} \).

Step2: Substitute the values into the formula

First, calculate \( \pi r^{2} \) for \( r = 6 \). \( \pi\times6^{2}=\pi\times36\approx3.14\times36 = 113.04 \) square inches. Then, find the fraction of the circle the sector represents: \( \frac{120}{360}=\frac{1}{3} \). Now, multiply this fraction by the area of the circle: \( A=\frac{1}{3}\times113.04 = 37.68\approx37.7 \) square inches.

Answer:

37.7 in²