Consider circle T with radius 24 in. and θ = 5pi/6 radians. What is the length of minor arc SV?

20π in.
28π in.
40π in.
63π in.

2 Answer

  • By definition, the arc length is given by:

    [tex] S = R * theta


    R: radius of the circle

    theta: central angle

    Therefore, substituting values we have:

    [tex] S = (24) * (\frac{5}{6}\pi)

    S = 20\pi

    Thus, the length of the minor arc SV is given by:

    20π in


    the length of minor arc SV is:

    20π in

    option 1

  • The length of the arc is equal to 20π in


    • θ = 5π/6 radians
    • radius = 24in

    Length of an Arc

    To find the length of the arc, we can either convert the angle from radians to degree and solve.

    [tex]1rad * 180/\pi = degree\\5\pi /6 * 180/\pi = ?\\5/6 * 180 = 150^0[/tex]

    The length of an arc is given as

    [tex]L_a_r_c= \frac{\theta}{360}*2\pi r\\ L_a_r_c = \frac{150}{360} *2\pi *24\\ L_a_r_c = 20\pi[/tex]

    From the calculation above, the length of the arc is equal to 20π.

    Learn more on length of an arc;