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Arc length = radius x angle: find the radius, angle or arc length

This type of question, asked 6 times: CDS 2 2017, CDS 1 2019, CDS 1 2020, CDS 2 2020, CDS 2 2023, CDS 2 2025. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2017

    81
    An arc of a circle subtends an angle π\pi at the centre. If the length of the arc is 22 cm, then what is the radius of the circle ? (Take π=227\pi = \frac{22}{7})

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  2. Question 2

    CDS 1 2019

    54
    A piece of wire of length 33 cm is bent into an arc of a circle of radius 14 cm. What is the angle subtended by the arc at the centre of the circle ?

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  3. Question 3

    CDS 1 2020

    84
    If an arc of a circle of radius 6 cm subtends a central angle measuring 30∘30^\circ, then which one of the following is an approximate length of the arc ?

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  4. Question 4

    CDS 2 2020

    53
    A road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 42∘42^\circ in distance of 44 m ? (Assume π=227\pi = \dfrac{22}{7})

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  5. Question 5

    CDS 2 2023

    55
    Two equal arcs of different circles C1C_1 and C2C_2 subtend angles of 60∘60^\circ and 75∘75^\circ respectively, at the centres. What is the ratio of the radius of C1C_1 to the radius of C2C_2 ?

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  6. Question 6

    CDS 2 2023

    61
    A pendulum swings through an angle of 9∘9^\circ and its end describes an arc of length 14.3 cm. What is the length of the pendulum ? (Take π=227\pi = \frac{22}{7})

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  7. Question 7

    CDS 2 2025

    76
    A pendulum swings through an angle of 30∘30^\circ and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take π=22/7\pi = 22/7)

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