Question

the radius of a circle is 1 kilometer. what is the length of a 135° arc?
135°
r=1 km
give the exact answer in simplest form.
kilometers

Explanation:

Step1: Recall arc length formula

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

Step2: Substitute values

Given \( \theta = 135^\circ \) and \( r = 1 \) km. Substitute these into the formula: \( L=\frac{135^\circ}{360^\circ}\times2\pi\times1 \).

Step3: Simplify the expression

Simplify \( \frac{135}{360}=\frac{3}{8} \), then \( L=\frac{3}{8}\times2\pi=\frac{3\pi}{4} \).

Answer:

\(\frac{3}{4}\pi\)