$\text{The chord length of a chord made on an arc of a circle is equal to the radius of the circle. The length of the arc is}\text{\_\_\_\_\_}\text{(in units), if the radius of the circle is}21\text{units. (Take}\pi =\frac{22}{7}\text{)}$

The correct answer is 22.

Step 1: Understand the given information
We are given:
Radius of the circle:
$r=21\text{units}$
Length of the chord:
$\text{Chord length}=21\text{units}$
Value of $\pi$:
$\pi =\frac{22}{7}$

Step 2: Find the central angle subtended by the arc
Consider the triangle formed by connecting the center of the circle to both endpoints of the chord.
The two sides connecting the center to the endpoints are radii of the circle, each having a length of $r=21$ units.
Since the length of the chord is also 21 units, all three sides of this triangle are equal.
Therefore, the triangle is an equilateral triangle.
In an equilateral triangle, each interior angle measures $60°$.
Thus, the central angle $\theta$ subtended by the arc at the center of the circle is:
$\theta =60°$

Step 3: Calculate the length of the arc
The formula for the length of an arc of a circle is:
$\text{Arc length}=\frac{\theta }{360°}\times 2\pi r$

Substituting the given values into the formula:
$\text{Arc length}=\frac{60}{360}\times 2\times \frac{22}{7}\times 21$

Simplifying step-by-step:
First, simplify the fraction $\frac{60}{360}$:

Next, divide 21 by 7:
$\text{Arc length}=\frac{1}{6}\times 2\times 22\times 3$
Multiply the factors in the numerator:
$\text{Arc length}=\frac{2\times 3\times 22}{6}$
$\text{Arc length}=\frac{6\times 22}{6}=22\text{units}$

Thus, the length of the arc is 22 units.