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Arc length = (angle/360) x 2 pi r: find arc, radius or angle (incl. part of a circumference)

This type of question, asked 12 times: 17 Jul 2023 S2, 19 Jul 2023 S1, 21 Jul 2023 S4, 12 Sep 2024 S3, 13 Sep 2024 S1, 17 Sep 2024 S1, 26 Sep 2024 S2, 12 Sep 2025 S2, 15 Sep 2025 S3, 17 Sep 2025 S2, 23 Sep 2025 S1, 26 Sep 2025 S3. All 12 questions below, oldest first.

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  1. Question 1

    17 Jul 2023 S2

    64
    An arc of length 23.1 cm subtends an 18∘18^\circ angle at the centre. What is the area of the circle? [Use π=227\pi = \frac{22}{7}]

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  2. Question 2

    19 Jul 2023 S1

    68
    Find the length of the arc of the sector of a circle of diameter 7 cm with a central angle of 108∘108^\circ. [Use π=227\pi = \frac{22}{7}]

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  3. Question 3

    21 Jul 2023 S4

    65
    An arc on a circle, whose length is 19.25 cm, subtends an 18∘18^\circ angle at the centre. What is the area of the circle? [Use π=227\pi = \frac{22}{7}.]

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  4. Question 4

    12 Sep 2024 S3

    75
    If the sectorial angle with radius 9.6 units is 75∘75^\circ, what is the length of the arc?

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  5. Question 5

    13 Sep 2024 S1

    53
    From a circle of radius 7 units, an arc length is cut by a chord of length 7 units. What is the arc length of the smaller portion (in units)?

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  6. Question 6

    17 Sep 2024 S1

    74
    At what angle is the arc length half the perimeter of the circle?

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  7. Question 7

    26 Sep 2024 S2

    68
    The central angle of a sector is 80∘80^\circ and whose length is 96π96\pi. What is the radius of the circle?

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  8. Question 8

    12 Sep 2025 S2

    69
    What is the central angle of a sector with an arc length of 10 cm in a circle of radius 5 cm?

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  9. Question 9

    15 Sep 2025 S3

    72
    A circular clock has a radius of 14 cm. Calculate the distance covered by the tip of the minute hand in 30 minutes, assuming it is positioned at the edge of the clock face? (Use π\pi= 22/7)

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  10. Question 10

    17 Sep 2025 S2

    66
    A circular garden has a diameter of 28 m. If a gardener wants to fence 75% of the garden's circumference, what length of fencing is needed? (Use π=22/7\pi = 22/7)

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  11. Question 11

    23 Sep 2025 S1

    68
    A circular jogging track has a radius of 50 m. A runner covers a curved path that subtends an angle of 120∘120^\circ at the center. What is the length of the arc she runs?

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  12. Question 12

    26 Sep 2025 S3

    56
    The angle subtended by an arc at the center is 72∘72^\circ, and its length is 22 cm. Find the radius of the circle.

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