Find the arc length subtended on a circle of radius 4 by a central angle of measure StartFraction pi Over 6 EndFraction
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Part 1
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To find the arc length subtended by a central angle, we use the formula for the arc length \( s \):

\[
s = r \theta
\]

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

Given:
- \( r = 4 \)
- \( \theta = \frac{\pi}{6} \)

Now, substitute the given values into the formula:

\[
s = 4 \times \frac{\pi}{6} = \frac{4\pi}{6} = \frac{2\pi}{3}
\]

So, the arc length is:

\[
s = \frac{2\pi}{3} \text{ units}
\]

Would you like more details or have any questions? Here are five related questions for further practice:

1. How would you calculate the arc length if the central angle was \( \frac{\pi}{4} \) and the radius was 3?
2. What is the relationship between arc length and the circumference of a circle?
3. If the radius is doubled, how does that affect the arc length for the same central angle?
4. How do you convert a central angle from degrees to radians?
5. How can you find the angle subtended if the arc length and radius are known?

**Tip:** Always make sure the angle is in radians when using the formula for arc length \( s = r \theta \).

Find the arc length subtended on a circle of radius 4 by a central angle of measure π/6.

Learn how to calculate the arc length of a circle with a radius of 4 and a central angle of π/6 radians. This problem uses the arc length formula s = rθ and covers key concepts from geometry and trigonometry. Suitable for students in Grades 9-12.

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