The length of the arc is 31.92 units
Explanation:
Given that the sector of a circle of radius 6 units.
The angle is given by [tex]\theta=305^{\circ}[/tex]
Arc length of the circle:
The arc length of the circle can be determined using the formula,
[tex]\ {arc\ length}=2 \pi r\left(\frac{\theta}{360}\right)[/tex]
where r = 6 and [tex]\theta=305^{\circ}[/tex]
Substituting the values, we have,
[tex]\ {arc\ length}=2 \pi (6)\left(\frac{305}{360}\right)[/tex]
Multiplying the numerator, we have,
[tex]\ {arc\ length}=\frac{3660 \pi}{360}[/tex]
Substituting [tex]\pi=3.14[/tex], we have,
[tex]\ {arc\ length}=\frac{3660(3.14)}{360}[/tex]
Multiplying the terms, we get,
[tex]\ {arc\ length}=\frac{11492.4}{360}[/tex]
Dividing, we get,
[tex]\ {arc\ length}=31.92 \ units[/tex]
Thus, the arc length of the circle is 31.92 units
