The length of a chord subtended by an arc of a circle is equal to the radius of the circle. If the radius of the circle is $21\text{units}$, then find the length of the arc (in units). (Take $\pi =\frac{22}{7}$)

Let the radius of the circle be $r=21\text{units}$.
**Step 1: Determine the central angle ($\theta$) subtended by the arc**
Given that the length of the chord is equal to the radius of the circle ($r$).
The triangle formed by the center of the circle and the two endpoints of the chord has all three sides equal to $r$. Thus, it forms an equilateral triangle.
The angle subtended at the center by this arc is $\theta =60^{\circ }$.

Step 2: Convert the angle into radians

$$\theta =60^{\circ }\times \frac{\pi }{180^{\circ }}=\frac{\pi }{3}\text{ radians}$$

**Step 3: Calculate the arc length ($l$)**
The formula for the length of an arc is:

$$l=r\theta$$

$$l=21\times \frac{\pi }{3}=7\pi$$

Substituting $\pi =\frac{22}{7}$:

$$l=7\times \frac{22}{7}=22\text{units}$$