Question

If a central angle of 5pie/3 is created with two radii that are 30 inches long then how long is the arc they will cut in radians

Answer 1

To find the length of the arc cut by a central angle in radians, you can use the formula for the arc length \( L \):

\[
L = r \theta
\]

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

In your case:
- The radius \( r = 30 \) inches,
- The central angle \( \theta = \frac{5\pi}{3} \) radians.

Now, substitute the values into the formula:

\[
L = 30 \times \frac{5\pi}{3}
\]

Now, simplify the calculation:

\[
L = 30 \times \frac{5\pi}{3} = 10 \times 5\pi = 50\pi
\]

Thus, the length of the arc is:

\[
L = 50\pi \text{ inches}
\]