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The problem involves finding the arc length of a circle. Here's how to solve it step by step:

### Given:
- Radius \( r = 4 \, \text{cm} \)
- Central angle \( \theta = 240^\circ \)

### Formula for Arc Length:
The arc length \( s \) of a circle can be found using the formula:
\[
s = r \theta
\]
Where:
- \( r \) is the radius of the circle
- \( \theta \) is the central angle in radians

Since the angle is given in degrees, we first need to convert it to radians using the conversion:
\[
\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180}
\]
Now, converting \( 240^\circ \) to radians:
\[
\theta_{\text{radians}} = 240^\circ \times \frac{\pi}{180} = \frac{4\pi}{3} \, \text{radians}
\]

### Calculate Arc Length:
Now, substitute the values into the arc length formula:
\[
s = 4 \times \frac{4\pi}{3} = \frac{16\pi}{3} \, \text{cm}
\]

### Approximation:
Using \( \pi \approx 3.1416 \), we can approximate the arc length:
\[
s \approx \frac{16 \times 3.1416}{3} \approx 16.755 \, \text{cm}
\]

Thus, the length of the arc is approximately **16.76 cm**.

Would you like any further details or have any questions?

Here are five related questions to expand your understanding:
1. How do you find the area of a sector for the same circle with a central angle of \(240^\circ\)?
2. What is the formula to calculate the circumference of a full circle?
3. How would the arc length change if the radius were doubled but the central angle remained the same?
4. How do you convert radians back into degrees?
5. What is the arc length if the central angle is a full circle, \(360^\circ\)?

### Tip:
Always remember to convert degrees to radians when using formulas that require angles in radians.

A circle has a radius of 4 cm. Find the length of the arc intercepted by a central angle of 240°.

Learn how to calculate the length of an arc for a circle with a radius of 4 cm and a central angle of 240°. This problem explains how to convert degrees to radians and apply the arc length formula. Perfect for students in Grades 7-9.

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