Question

If a circle has a radius of 6 cm and a central angle of 5π4 , then what is the length of the arc created by the angle?(1 point)

Answer 1

To find the length of the arc created by a central angle in a circle, we can use the formula:

\[
\text{Arc Length} = r \theta
\]

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

Given:
- Radius \( r = 6 \) cm,
- Central angle \( \theta = \frac{5\pi}{4} \) radians.

Now, substituting these values into the formula:

\[
\text{Arc Length} = 6 \cdot \frac{5\pi}{4}
\]

Calculating this, we have:

\[
\text{Arc Length} = \frac{6 \cdot 5\pi}{4} = \frac{30\pi}{4} = \frac{15\pi}{2}
\]

Thus, the length of the arc is:

\[
\frac{15\pi}{2} \text{ cm}
\]

So, the final answer is:

\(\frac{15\pi}{2}\) cm.