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IB Mathematics: Applications and Interpretation HL · 12.10: Geometry & Trigonometry · 12.10.12

Name Date

Arc length and sector area Problem set A

Sketch each shape. Give lengths and areas to 3 significant figures, with units.

Difficulty: first skills applying them stretch

Skills

  1. A sector has radius 7.2 cm and angle 115° at the centre. Find the length of its arc.

    115°7.2 cmOAB

  2. A sector has radius 11 cm and angle 72° at the centre. Find its area.

    72°11 cmOAB

  3. An arc of length 15 cm subtends an angle of 70° at the centre of a circle. Find the radius of the circle.

    70°r15 cmOAB

  4. A sector of radius 7 cm has area 40 cm². Find the angle at the centre.

    θ7 cmOAB

  5. A sector has radius 8 cm and angle 0.7 radians at the centre. Find

    0.7 rad8 cmOAB
    1. (a) the arc length
    2. (b) the area of the sector

In context

  1. A designer cuts a segment from a circular metal disc of radius 9 cm. The straight edge AB subtends an angle of 75° at the centre O. Find

    75°9 cmOAB
    1. (a) the perimeter of the segment
    2. (b) the area of the segment

  2. A lawn sprinkler sprays water up to 6.5 m and sweeps through 130°. Find

    130°6.5 mOAB
    1. (a) the area of the region
    2. (b) the total length of its edge (the arc and the two straight sides)

  3. A horse is tied by an 8 m rope to the outside corner of a barn that is 11 m by 14 m. The horse can graze only outside the barn. Find the area it can reach.

    270°8 mX

  4. A point P on the rim of a bicycle wheel of radius 0.34 m moves in a circle about the axle. The wheel turns at 9.5 radians per second.

    1. (a) Find the distance P travels in 4 seconds.
    2. (b) Find the speed of P in m s⁻¹ and in km/h.
    3. (c) Find the time for one complete turn.

Stretch

  1. A circular pond has radius 10 m. A straight path AB of length 14 m cuts off a segment of the pond. Find

    θ10 mOAB
    1. (a) the angle AOB at the centre
    2. (b) the area of the segment

  2. A sector has a perimeter of 20 cm and an angle of 1.2 radians at the centre. Find

    1. (a) the radius r
    2. (b) the area of the sector

jmaths.xyz · AI HL · 12.10.12 Arc length and sector area