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# A circle with a radius of 6 meters has an are that measures $35^{\circ}$. If this arc and its associated sector are completely removed from the circle, what is the length of the major are that remains, to the nearest tenth of a meter?

Solution

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Determine the measurement of the arc left after removal of the $35\text{\textdegree}$ arc.

$\begin{gather*} 360 - 35 = 325 \end{gather*}$

Determine the length of the major arc left. Use the circumference formula.

\begin{align*} &= 2 \pi r \times \dfrac{325}{360} && \text{Write an expression}\\ &= 2(3.14)(6) \times \dfrac{325}{360} && \text{Substitute the values}\\ &= 37.68 \times \dfrac{325}{360} && \text{Multiply the values}\\ &= 34.0 && \text{Multiply the values} \end{align*}

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