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UnholySheep · Answer 1 · 2023-02-14T17:29:09+0000

The answer is 16.90cm

The figure given is a circle divided into two sectors. We are required to find the length of the major arc which is in bold.

The formula for finding the length of arc is:

$\begin{gathered} \text{length of arc=}(\theta)/(360)*2\pi r \\ \\ r=\text{radius of circle} \\ \theta=\text{angle subtended by the arc.} \end{gathered}$

We are given the radius of the circle as 4cm

While we are given the angle subtended by the minor arc as 118

The angle (M) subtended by the major arc can be gotten by:

$\begin{gathered} <p>Now that we have the angle subtended at the center by the major arc, we can now proceed to solve for the length of the arc:</p><p></p>[tex]\begin{gathered} Length=(M)/(360)*2*\pi* r \\ \\ \text{Length}=(242)/(360)*2*\pi*4=16.895\operatorname{cm} \\ \\ \therefore\text{Length=}16.90\text{ (to two decimal places)} \end{gathered}$

Therefore, the answer is 16.90cm

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