Question

a circle has a radius of 48 millimeters.
what is the length of the arc intercepted by a central angle that measures \frac{3\pi}{4} radians?
express the answer in terms of \pi.
enter your answer in the box.
mm

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s = r\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

Given \(r = 48\) mm and \(\theta=\frac{3\pi}{4}\) radians.
Substitute into \(s = r\theta\): \(s=48\times\frac{3\pi}{4}\).

Step3: Simplify the expression

First, simplify \(48\times\frac{3\pi}{4}\).
\(48\div4 = 12\), then \(12\times3\pi=36\pi\).

Answer:

\(36\pi\)