Question

what is the length of an arc subtended by a central angle of 60° in a circle of radius 7? a. 44 cm b. 25.6 cm c. 22 cm d. 7.3 cm

Explanation:

Step1: Write the formula for arc length

The formula for arc length \(l\) is \(l=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle.

Step2: Substitute the given values

Given \(\theta = 60^{\circ}\) and \(r = 7\). Substitute into the formula: \(l=\frac{60}{360}\times2\pi\times7\).
Simplify \(\frac{60}{360}=\frac{1}{6}\), then \(l=\frac{1}{6}\times2\pi\times7=\frac{7\pi}{3}\).
Take \(\pi\approx3.14\), so \(l=\frac{7\times3.14}{3}\approx7.3\)

Answer:

d. \(7.3\) cm