A circle with r and a central angle θ. If r=36 meters and the central angle θ=7π/9 radians, then the length of the circular arc subtending the central angle is?

To find the length of the circular arc subtending the central angle \(\theta\), you can use the formula:

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

Given:
- \( r = 36 \) meters
- \( \theta = \frac{7\pi}{9} \) radians

Now, plug in the values:

\[
\text{Arc Length} = 36 \times \frac{7\pi}{9}
\]

Simplify the expression:

\[
\text{Arc Length} = \frac{36 \times 7\pi}{9} = \frac{252\pi}{9} = 28\pi \text{ meters}
\]

So, the length of the circular arc is \( 28\pi \) meters.

Would you like more details on any part of this solution or have any other questions?

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Here are some related questions you might find useful:
1. What is the area of the sector formed by the same central angle \(\theta\)?
2. How would the arc length change if the radius were doubled?
3. What is the formula for the arc length if \(\theta\) is measured in degrees?
4. How do you convert between radians and degrees for a given angle?
5. How does the arc length formula relate to the circumference of a circle?

**Tip:** Always remember that in the formula \(\text{Arc Length} = r \times \theta\), \(\theta\) must be in radians, not degrees.

Learn how to calculate the length of a circular arc subtending a central angle of 7π/9 radians with a radius of 36 meters. Understand the application of the arc length formula in trigonometry. Suitable for high school students and anyone interested in geometry and trigonometry.

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