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The problem asks for the length of the arc \( s \) cut off by the central angle \( \theta = 30^\circ \) in a circle of radius \( r = 4 \text{ mm} \).

### Formula to Find the Arc Length:
The formula to calculate the arc length \( s \) is:
\[
s = r \theta
\]
where \( r \) is the radius of the circle, and \( \theta \) is the central angle in radians.

### Step 1: Convert the Angle to Radians
Since the angle is given in degrees, we need to convert it to radians. The conversion formula is:
\[
\theta \text{(radians)} = \theta \text{(degrees)} \times \frac{\pi}{180^\circ}
\]

So, for \( \theta = 30^\circ \):
\[
\theta = 30^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{6} \, \text{radians}
\]

### Step 2: Calculate the Arc Length
Now, substitute \( r = 4 \text{ mm} \) and \( \theta = \frac{\pi}{6} \) into the arc length formula:
\[
s = 4 \times \frac{\pi}{6} = \frac{4\pi}{6} = \frac{2\pi}{3} \, \text{mm}
\]

Thus, the arc length is:
\[
s = \frac{2\pi}{3} \approx 2.094 \, \text{mm}
\]

Would you like more details on this calculation or have any specific questions?

### Related Questions:
1. How do you convert a radian measure back into degrees?
2. What is the formula for calculating the area of a sector for a given central angle?
3. How does the arc length change if the radius of the circle is doubled?
4. What happens to the arc length if the angle \( \theta \) is halved?
5. How would you calculate the perimeter of a sector formed by the central angle?

### Tip:
Always ensure that angles are in radians when using formulas related to arc length and sector area.

For each of the following problems, θ is a central angle in a circle of radius r. In each case, find the length of arc s cut off by θ, where θ = 30° and r = 4 mm.

Find the length of the arc cut off by a central angle of 30° in a circle of radius 4 mm. Learn how to convert degrees to radians and use the arc length formula for detailed calculation. Suitable for students in Grades 8-10.

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