Question

a sector of a circle has a central angle of 30°. find the area of the sector if the radius of the circle is 13 cm. cm² question help: video

Explanation:

Step1: Write the formula for the area of a sector

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

Step2: Substitute the given values

Given \(\theta = 30^{\circ}\) and \(r = 13\) cm. Substitute into the formula: \(A=\frac{30}{360}\times\pi\times(13)^{2}\).

Step3: Simplify the expression

First, \(\frac{30}{360}=\frac{1}{12}\). Then \(A=\frac{1}{12}\times\pi\times169\).
\(A=\frac{169\pi}{12}\approx\frac{169\times3.14}{12}\)
\(A=\frac{530.66}{12}\approx44.22\)

Answer:

\(44.22\)