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 $L = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.

Step2: Substitute values

Here, $\theta = 90^\circ$ and $r = 2$ km. Substitute these into the formula: $L = \frac{90^\circ}{360^\circ} \times 2\pi \times 2$.

Step3: Simplify the expression

Simplify $\frac{90}{360} = \frac{1}{4}$. Then the expression becomes $\frac{1}{4} \times 4\pi$ (since $2\times2 = 4$). The 4 in the numerator and denominator cancels out, leaving $L = \pi$.

Answer:

$\pi$