Solve For The Arc Length Of The Given Circle Below. Use 03c0 = 3.14.

Solve for the arc length of the given circle below. Use π = 3.14.

✏️ARC LENGTH

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Problem: Solve for the arc length of the given circle below. Use π = 3.14.

Solution: Find the length of the arc in which it is the product of the ratio of the angle subtended to it at 360 degrees, and the circles circumference.

$\begin{aligned}& \bold{ \color{lightblue}Formula: } \\ & \boxed{ \ell = \frac{ \theta}{360 \degree} \cdot2\pi r } \end{aligned}$

- The diameter of the circle is twice its radius, thus we can say that the circumference of the circle is the product of its diameter and pi.

$\ell = \frac{110 \degree}{360 \degree} \cdot2\pi(4) \\$

$\ell = \frac{22}{72} \cdot\pi(8) \\$

$\ell = \frac{ \pi(176)}{72} \\$

$\ell = \pi(2.44)$

- Let 3.14 be the approximate value of pi.

$\ell = (3.14)(2.44)$

$\ell = 7.66$

- Therefore, the length of the arc is:

$\large \rm Arc \: Length = \boxed{ \rm \green{ \: 7.66 \: }}$

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