Question

The diagram shows a sector of a circle of radius 6 units, formed from an angle of size 305°.

Answer 1

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 $\theta=305^{\circ}$

Arc length of the circle:

The arc length of the circle can be determined using the formula,

$\ {arc\ length}=2 \pi r\left(\frac{\theta}{360}\right)$

where r = 6 and $\theta=305^{\circ}$

Substituting the values, we have,

$\ {arc\ length}=2 \pi (6)\left(\frac{305}{360}\right)$

Multiplying the numerator, we have,

$\ {arc\ length}=\frac{3660 \pi}{360}$

Substituting $\pi=3.14$, we have,

$\ {arc\ length}=\frac{3660(3.14)}{360}$

Multiplying the terms, we get,

$\ {arc\ length}=\frac{11492.4}{360}$

Dividing, we get,

$\ {arc\ length}=31.92 \ units$

Thus, the arc length of the circle is 31.92 units