Question

Find the length of the arc for a circle with a radius of 18 inches and a central angle of 300degrees leave your answer in terms of pi

Answer 1

To find the length of an arc of a circle, you can use the formula:

\[
L = r \theta
\]

where:
- \( L \) is the length of the arc,
- \( r \) is the radius of the circle, and
- \( \theta \) is the central angle in radians.

First, we need to convert the central angle from degrees to radians. The conversion from degrees to radians is given by:

\[
\theta \text{ (in radians)} = \theta \text{ (in degrees)} \times \frac{\pi}{180}
\]

So for a central angle of 300 degrees:

\[
\theta = 300 \times \frac{\pi}{180} = \frac{300\pi}{180} = \frac{5\pi}{3} \text{ radians}
\]

Now we can substitute \( r = 18 \) inches and \( \theta = \frac{5\pi}{3} \) radians into the arc length formula:

\[
L = 18 \times \frac{5\pi}{3}
\]

Calculating this gives:

\[
L = \frac{18 \times 5\pi}{3}
\]

Simplifying further:

\[
L = \frac{90\pi}{3} = 30\pi
\]

Thus, the length of the arc is

\[
\boxed{30\pi} \text{ inches.}
\]