Question

what is the length of the arc shown in red?
the length of the arc is □ cm.
(simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall the arc - length formula

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

Step2: Substitute the given values

Here, \(r = 6\) cm and \(\theta=45^{\circ}\).
Substitute into the formula: \(s=\frac{45}{360}\times2\pi\times6\).
First, simplify \(\frac{45}{360}=\frac{1}{8}\).
Then, \(s=\frac{1}{8}\times2\pi\times6\).
\(2\times6 = 12\), so \(s=\frac{12\pi}{8}\).
Simplify \(\frac{12\pi}{8}=\frac{3\pi}{2}\) cm.

Answer:

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