In a circle of radius 21 cm, an arc subtends an angle of $60^{o}$ at the center. Find $( 1)$. The length of the arc $( 2)$ Area of the sector formed by the arc. [use $\pi =\frac{22}{7}$].

Given: An arc subtends an angle of $60^{o}$ at the center of a circle with radius$21\ cm$.

To do: To Find $( 1)$. the length of the arc, $( 2)$ area of the sector formed by the arc.

Solution:
As given in the question,

Radius of the circle, $r=21\ cm$

Angle subtended at the center by the arc $=60^{o}$

$( 1)$ . The length of the arc$=\frac{\theta }{360^{o}} \times 2\pi r$

$=\frac{60^{o}}{360^{o}} \times 2\times \frac{22}{7} \times 21$

$=22\ cm$

$( 2)$ .Area of the sector formed by the arc$=\frac{\theta }{360^{o}} \times \pi r^{2}$

$=\frac{60^{o}}{360^{o}} \times \frac{22}{7} \times 21\times 21$

=231cm^{2}

Therefore, Length of the arc $=22\ cm$ and  area of the sector formed by the arc $=231\ cm^{2}$.
 

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Updated on: 10-Oct-2022

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