Question

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)

Remaining Attempts : 3

Answer 1

To find the length of the arc (s) created by a central angle in a circle, you can use the formula:

\[
s = r \cdot \theta
\]

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

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

Now, substitute the values into the formula:

\[
s = 6 \cdot \frac{5\pi}{4}
\]

Calculating it:

\[
s = \frac{30\pi}{4} = \frac{15\pi}{2}
\]

Now, you can find an approximate decimal value for \(s\) if needed by substituting \(\pi \approx 3.14\):

\[
s \approx \frac{15 \times 3.14}{2} \approx 23.55 \text{ cm}
\]

Thus, the exact length of the arc is:

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

And if you require an approximate numerical value:

\[
s \approx 23.55 \text{ cm}
\]