Question

the radius of a circle is 10 kilometers. what is the length of a 90° arc?
90°
r=10 km
give the exact answer in simplest form.
kilometers

Explanation:

Step1: Recall arc length formula

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

Step2: Substitute values

Here, \(\theta = 90^\circ\) and \(r = 10\) km. Substitute these into the formula:
\(L=\frac{90^\circ}{360^\circ}\times2\pi\times10\)

Step3: Simplify the expression

Simplify \(\frac{90}{360}=\frac{1}{4}\), so:
\(L=\frac{1}{4}\times20\pi\)
\(L = 5\pi\)

Answer:

\(5\pi\)