Question

which formula is used to find the area of a sector?
a. a = \frac{1}{2}\theta r^{2}
b. a = 2\pi r
c. a = \pi r^{3}
d. a = \theta r

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 radians) is \(A=\frac{1}{2}\theta r^{2}\).

Step2: Analyze each option

• Option a: \(A = \frac{1}{2}\theta r^{2}\) is the correct formula for the area of a sector.
• Option b: \(A=2\pi r\) is the formula for the circumference of a circle.
• Option c: \(A=\pi r^{3}\) is not a standard formula related to circle - related measurements (area of a circle is \(A = \pi r^{2}\), volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\)).
• Option d: \(A=\theta r\) is the formula for the arc length \(s\) of a sector (\(s=\theta r\) where \(\theta\) is in radians).

Answer:

a. \(A=\frac{1}{2}\theta r^{2}\)