ind the radius *r* of the circle if an arc of length 6 m on the circle subtends a central angle of 3𝜋/7 rad. (Round your answer to two decimal places.)

To find the radius \( r \) of the circle, you can use the formula relating the arc length \( s \), the radius \( r \), and the central angle \( \theta \) (in radians):

\[
s = r \theta
\]

Given:
- Arc length, \( s = 6 \) m
- Central angle, \( \theta = \frac{3\pi}{7} \) rad

We need to find the radius \( r \). Rearrange the formula to solve for \( r \):

\[
r = \frac{s}{\theta}
\]

Substitute the values:

\[
r = \frac{6}{\frac{3\pi}{7}} = \frac{6 \times 7}{3\pi} = \frac{42}{3\pi}
\]

Now, calculate \( r \) and round to two decimal places:

\[
r = \frac{42}{3\pi} \approx \frac{42}{9.4248} \approx 4.46 \text{ m}
\]

So, the radius \( r \) is approximately **4.46 meters**.

Would you like further details or have any questions?

Here are 5 related questions for you to explore:
1. How would the radius change if the central angle were doubled?
2. What is the formula for arc length if the angle is given in degrees?
3. How do you convert a central angle from radians to degrees?
4. What is the relationship between the circumference of a circle and the central angle for a full circle?
5. How would the radius change if the arc length were halved?

**Tip:** Always ensure the central angle is in radians when using the arc length formula.

Discover how to find the radius of a circle when given an arc length of 6 meters and a central angle of 3π/7 radians. Follow a step-by-step solution using the arc length formula. Suitable for high school students learning about circle geometry and arc measurements.

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