Find the area (in cm²) of the sector of a circle of radius 21 cm with a central angle of 60°. [Use $\pi =\frac{22}{7}$ ]

The correct answer is 231.

Given parameters:
Radius of the circle, $r=21\text{cm}$
Central angle, $\theta =60°$
Value of $\pi =\frac{22}{7}$

Formula:
The area of a sector of a circle with radius $r$ and central angle $\theta$ is given by:

$\text{Area of sector}=\frac{\theta }{360°}\times \pi \times r^2$

Step-by-step Calculation:

Substitute the given values into the formula:

$\text{Area of sector}=\frac{60}{360}\times \frac{22}{7}\times {21}^2$

Simplify the fraction $\frac{60}{360}=\frac{1}{6}$:

$\text{Area of sector}=\frac{1}{6}\times \frac{22}{7}\times 21\times 21$

Divide 21 by 7 to get 3:

$\text{Area of sector}=\frac{1}{6}\times 22\times 3\times 21$

Simplify $\frac{3\times 22}{6}=\frac{66}{6}=11$:

$\text{Area of sector}=11\times 21$

$\text{Area of sector}=231{\text{cm}}^2$

Thus, the area of the sector of the circle is 231 cm².