if an arc of 60 degrees has an arc length of 50pi what is the circumference

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if an arc of 60 degrees has an arc length of 50pi what is the circumference

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Samantha 3 months 2022-02-15T07:04:33+00:00 1 Answer 0 views 0

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    2022-02-15T07:05:34+00:00

    Answer: 300[tex]\pi[/tex]

    Step-by-step explanation:

    Let’s use the arc-length formula to solve this problem, and plug in the values that we have. Arc length is 50[tex]\pi[/tex] and the arc is 60°

    Arc-length = [tex]2\pi r (\frac{x}{360})[/tex]

    [tex]50\pi =2\pi r(\frac{60}{360})[/tex]

    Cancel the [tex]\pi[/tex] and simplify the fraction.

    [tex]50 = 2r(\frac{1}{6})[/tex]

    Simplify further.

    [tex]50 = r(\frac{1}{3} )[/tex]

    Pass the 3 to the other side.

    [tex]150=r[/tex]

    So our radius is 150.

    To find the circumference, we use the formula [tex]2\pi r[/tex]

    Plug in r.

    [tex]2\pi (150) = 300\pi[/tex]

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