Question

the diameter of a circle is 12 meters. what is the length of a 45° arc?
d=12 m
45°
give the exact answer in simplest form.
meters
π

Explanation:

Step1: Find the radius

The radius \( r \) of a circle is half of the diameter. Given \( d = 12\) meters, so \( r=\frac{d}{2}=\frac{12}{2} = 6\) meters.

Step2: Use the arc - length formula

The formula for the length of an arc \( s\) is \( s=\frac{\theta}{360}\times2\pi r\), where \( \theta = 45^{\circ}\) and \( r = 6\) meters.
Substitute the values into the formula:

$$
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Answer:

\(\frac{3\pi}{2}\)