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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 B

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

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. A cake slice is a sector of radius 9.4 cm and angle 48° at the centre. Find the length of its curved edge.

    48°9.4 cmOAB

  2. A fan is a sector with radius 8.5 cm and angle 130° at the centre. Find its area.

    130°8.5 cmOAB

  3. A curved fence of length 22 m is part of a circle and subtends an angle of 105° at the centre. Find the radius of the circle.

    105°r22 mOAB

  4. A pizza slice of radius 8 cm has area 55 cm². Find the angle at the centre.

    θ8 cmOAB

  5. A wedge of a clock face has radius 6 cm and angle 1.4 radians at the centre. Find

    1.4 rad6 cmOAB
    1. (a) the arc length
    2. (b) the area of the sector

In context

  1. A baker cuts a segment from a circular pastry of radius 14 cm. The straight cut AB subtends an angle of 80° at the centre O. Find

    80°14 cmOAB
    1. (a) the perimeter of the segment
    2. (b) the area of the segment

  2. A lighthouse beam reaches 12 km and sweeps through 110°. Find

    110°12 kmOAB
    1. (a) the area of the region
    2. (b) the total length of its edge (the arc and the two straight sides)

  3. A llama is tied by a 6 m rope to the outside corner of a hut that is 9 m by 8 m. The llama can graze only outside the hut. Find the area it can reach.

    270°6 mX

  4. The tip P of a ceiling fan blade is 0.22 m from the centre of the fan. The fan turns at 14 radians per second.

    1. (a) Find the distance P travels in 3 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 flower bed has radius 12 m. A straight fence AB of length 16 m cuts off a segment of the bed. Find

    θ12 mOAB
    1. (a) the angle AOB at the centre
    2. (b) the area of the segment

  2. A sector has a perimeter of 18 cm and an angle of 0.8 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