To find the radius $r$ of the circle given the arc length and the central angle, we use the formula:

$r = \frac{s}{\theta}$

where:

• $s = 21$ meters (arc length),
• $\theta = \frac{7\pi}{9}$ radians (central angle).

Substituting the values:

$r = \frac{21}{\frac{7\pi}{9}} = \frac{21 \times 9}{7\pi} = \frac{189}{7\pi}$

Calculating the radius, $r \approx 8.59$ meters.

Would you like further details or have more questions?

Related Questions:

1. What formula would you use if the angle was given in degrees instead of radians?
2. How would the arc length change if the radius doubled?
3. What is the circumference of the circle with radius $r = 8.59$ meters?
4. How does the arc length relate to the circumference for a full circle?
5. How would you calculate the central angle if the arc length and radius are known?

Tip: Always ensure the angle is in radians when using the arc length formula for a circle.