Question

the radius of a circle is 20 inches. what is the length of a 180° arc?
r=20 in
180°
give the exact answer in simplest form.
inches
π

Explanation:

Step1: Recall arc length formula

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

Step2: Identify given values

Here, \( \theta = 180^\circ \) and \( r = 20 \) inches.

Step3: Substitute values into formula

Substitute \( \theta = 180^\circ \) and \( r = 20 \) into the formula:
\( s=\frac{180^\circ}{360^\circ}\times2\pi\times20 \)
Simplify \( \frac{180^\circ}{360^\circ}=\frac{1}{2} \), so:
\( s=\frac{1}{2}\times2\pi\times20 \)
The \( 2 \) in the numerator and denominator cancels out:
\( s = \pi\times20=20\pi \)

Answer:

\( 20\pi \)