Question

find the area of the sector of the circle.
r = 8.86 cm, θ = 123°

a. 168.59 cm²
b. 337.17 cm²
c. 9.51 cm²
d. 84.26 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

Given \(r = 8.86\space cm\) and \(\theta=123^{\circ}\).
Substitute into the formula: \(A=\frac{123}{360}\times\pi\times(8.86)^{2}\).
First, calculate \((8.86)^{2}=78.4996\).
Then, \(\frac{123}{360}\times\pi\times78.4996=\frac{123\times78.4996\pi}{360}\).
\(123\times78.4996 = 9655.4408\).
\(\frac{9655.4408\pi}{360}\approx\frac{9655.4408\times3.1416}{360}\).
\(9655.4408\times3.1416\approx30332.53\).
\(\frac{30332.53}{360}\approx84.26\space cm^{2}\).

Answer:

D. \(84.26\space cm^{2}\)