Find the length of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30°

Question

Find the length of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30°

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    0
    2021-09-14T22:41:10+00:00

    Answer:

    Let s be the length of the arc subtending an angle \sf{\theta}^{c} at the centre of a circle of radius r.

    Then,

     \\  \theta \:  =  \sf \:  \frac{s}{r} \\

    Here,

    • r = 12 cm.
    • ∅ = 30°

     \\  \implies \sf \:  \bigg(30 \times  \frac{\pi}{180}  \bigg) {}^{c}  \\  \\  \\  \implies \sf \blue{  \bigg({ \frac{\pi}{6} } \bigg)^{c}  } \\

    Therefore,

     \\  \theta =  \sf \:  \dfrac{s}{r}  \\  \\  \\  \implies \sf \:  \frac{\pi}{6}  =  \frac{s}{12}  \\  \\  \\  \implies \sf \red{s =  \frac{12\pi}{6} cm. }   \\

    0
    2021-09-14T22:41:20+00:00

    Formula for arc lenght:
    l =  \frac{ \alpha }{360} 2r\pi
    Insert given data:
    l =  \frac{30}{360} \times  2 \times 12cm \times \pi
    l = 2\pi  = 6.28cm

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