Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 months ago

A circle has a radius of 9 cm. A central angle measures 315 degrees. ?

Determine the arc lenth subtended by two radii making the central angle. Round your answer to the nearest tenth of a centimeter.

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  • sepia
    Lv 7
    8 months ago

    A circle has a radius of 9 cm.

    A central angle measures 315 degrees.

    Determine the arc length subtended by two radii making the central angle.

    2 pi * 9 (315/360) cm = 49.4800843 cm or

    49.5 cm (rounded to the nearest tenth of a centimeter).  

  • Anonymous
    8 months ago

    315 / 360 * pi * radius

  • 8 months ago

    What's the circumference of a full circle with a 9 cm radius?

    C = 2πr

    C = 2π*9

    C = 18π cm

    But you don't want a full 360°, you just want 315°. So multiply by 315/360. We can reduce that fraction if you like by dividing top and bottom by 45.

    315/360

    = 7/8

    So take 7/8 of the full circumference:

    arc = 7/8 * 18π cm

    arc = 7/4 * 9π cm

    arc = 63π / 4

    arc ≈  49.48 cm

    Answer (to the nearest tenth of a centimeter)

    ~49.5 cm

  • 8 months ago

    s = rθ, where θ is measured in radians.

    θ = (315 / 180)π radians = 7π/4 radians

    s = 9(7π/4) = 63π/4 = 49.5 cm

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  • 2 * pi * 9 * (315/360) =>

    18 * pi * (7/8) =>

    9 * pi * 7 / 4 =>

    63 * pi / 4 =>

    49.4800...

    49.5

    Or

    (63/4) * pi =>

    (63/4) * (22/7), roughly

    (63/7) * (22/4) =>

    9 * 11/2 =>

    99/2 =>

    49.5

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