Question

the diameter of a circle is 6 meters. what is the length of a 30° arc?
d=6 m
30°
give the exact answer in simplest form.

Explanation:

Step1: Find the circumference

The formula for the circumference of a circle is \( C = \pi d \), where \( d \) is the diameter. Given \( d = 6 \) meters, so \( C=\pi\times6 = 6\pi \) meters.

Step2: Calculate the arc length

The arc length formula for a central angle \( \theta \) (in degrees) is \( \text{Arc Length}=\frac{\theta}{360^\circ}\times C \). Here, \( \theta = 30^\circ \) and \( C = 6\pi \). So, \( \text{Arc Length}=\frac{30^\circ}{360^\circ}\times6\pi \). Simplify \( \frac{30}{360}=\frac{1}{12} \), then \( \frac{1}{12}\times6\pi=\frac{6\pi}{12}=\frac{\pi}{2} \) meters.

Answer:

\(\frac{\pi}{2}\) meters