We are given that a sector of a circle has a radius of 21 cm and subtends an angle of $120^{\circ}$ at the center. We need to find the length of the arc of this sector, using $\pi = \frac{22}{7}$.

1. Problem Description

We are given that a sector of a circle has a radius of 21 cm and subtends an angle of $120^{\circ}$ at the center. We need to find the length of the arc of this sector, using $\pi = \frac{22}{7}$.

2. Solution Steps

The formula for the length of an arc of a sector is given by:

$Arc\,length = \frac{\theta}{360^{\circ}} \times 2\pi r$

where $\theta$ is the angle subtended at the center and $r$ is the radius of the circle.

In this problem, $\theta = 120^{\circ}$ and $r = 21$ cm. We are also given that $\pi = \frac{22}{7}$. Substituting these values into the formula, we get:

$Arc\,length = \frac{120}{360} \times 2 \times \frac{22}{7} \times 21$

$Arc\,length = \frac{1}{3} \times 2 \times \frac{22}{7} \times 21$

$Arc\,length = \frac{1}{3} \times 2 \times 22 \times 3$

$Arc\,length = 2 \times 22$

$Arc\,length = 44$ cm

3. Final Answer

44 cm