Question

If a circle has a central angle of π3
and a radius of 5 mm. How long is the arc formed by that angle?
A
S
200
B
3
5
(1 point)
Responses

25π3
25pi over 3

35π
3 over 5 pi

15π
15pi

5π3

Answer 1

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

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

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

In your case:
- \( r = 5 \) mm
- \( \theta = \frac{\pi}{3} \) radians

Now, substituting these values into the formula:

\[
\text{Arc Length} = 5 \cdot \frac{\pi}{3} = \frac{5\pi}{3} \, \text{mm}
\]

So the length of the arc is \(\frac{5\pi}{3}\) mm.

Therefore, the correct answer choice is:

**5π3** (which matches your format \(\frac{5\pi}{3}\)).