Question

the radius of a circle is 2 kilometers. what is the length of a 90° arc?
90°
r=2 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 \( \theta = 90^\circ \) and \( r = 2 \) km. Substitute these into the formula: \( L=\frac{90^\circ}{360^\circ}\times2\pi\times2 \).

Step3: Simplify the expression

Simplify \( \frac{90^\circ}{360^\circ}=\frac{1}{4} \), then \( L=\frac{1}{4}\times4\pi \). The 4 in the numerator and denominator cancels out, leaving \( L = \pi \).

Answer:

\( \pi \)