Question

if a sector has a central angle of 120° and a radius of 3 meters, what is the area of this sector?
a. 3π square meters
b. 9π square meters
c. 2π square meters
d. 6π square meters

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector is \(A=\frac{\theta}{360^{\circ}}\times\pi r^{2}\), where \(\theta\) is the central angle and \(r\) is the radius.

Step2: Substitute the given values into the formula

Given \(\theta = 120^{\circ}\) and \(r = 3\) meters. Then \(A=\frac{120^{\circ}}{360^{\circ}}\times\pi\times(3)^{2}\).
Simplify \(\frac{120^{\circ}}{360^{\circ}}=\frac{1}{3}\), and \((3)^{2}=9\). So \(A=\frac{1}{3}\times\pi\times9\).

Step3: Calculate the value of the area

\(A = 3\pi\) square meters.

Answer:

a. \(3\pi\) square meters