G18 calculate arc lengths, angles and areas of sectors of circles Quiz: Pearson Edexcel Maths, Unit 4

The 20 questions

1. The arc length of a sector with angle θ in degrees and radius r is:

   • 2πr × θ
   • (θ/90) × πr
   • (θ/360) × πr²
   • (θ/360) × 2πr

2. The area of a sector with angle θ and radius r is:

   • (θ/360) × πr²
   • (θ/180) × 2r
   • πr² × θ
   • (θ/360) × 2πr

3. A sector with a central angle of 360° is:

   • a segment
   • a semicircle
   • a quadrant
   • a full circle

4. A quarter-circle sector has a central angle of:

   • 180°
   • 45°
   • 60°
   • 90°

5. What term describes the distance along the curved edge of a circle?

   • Circumference
   • Sector area
   • Arc length
   • Chord length

6. An arc length is a fraction of:

   • the diameter
   • the circumference
   • the area
   • the radius

7. Where is the interior angle of a circle sector always located?

   • On the circumference
   • At a tangent
   • Across the chord
   • At the centre

8. Which two variables directly cause an increase in arc length?

   • Angle and pi
   • Diameter and area
   • Radius and angle
   • Radius and chord

9. A sector has radius 10 cm and angle 72°. What is its arc length in terms of π?

   • 4π cm
   • 2π cm
   • 7.2π cm
   • 20π cm

10. A sector has radius 6 cm and angle 120°. What is its area in terms of π?

    • 12π cm²
    • 36π cm²
    • 4π cm²
    • 24π cm²

11. A sector has radius 9 cm and angle 40°. What is its arc length in terms of π?

    • 2π cm
    • 9π cm
    • 4π cm
    • 0.5π cm

12. A sector has area 10π cm² and angle 90°. What is its radius?

    • 2√10 cm
    • 10 cm
    • 5 cm
    • √20 cm

13. A sector has radius 5 cm and angle 60°. What is its perimeter in terms of π?

    • 10 + 5π/3 cm
    • 10 + 5π cm
    • 10 + 10π/3 cm
    • 5π/3 cm

14. A sector has radius 12 cm and area 24π cm². What is its angle?

    • 60°
    • 120°
    • 90°
    • 30°

15. A minute hand of radius 9 cm turns through 150°. What is the arc length it traces, in terms of π?

    • 2.5π cm
    • 7.5π cm
    • 18π cm
    • 15π cm

16. A sector has radius 4 cm and angle 90°. What is the area of the segment formed by the sector and its chord, in exact form?

    • 4π + 8 cm²
    • 8π − 8 cm²
    • 8π cm²
    • 4π − 8 cm²

17. Two sectors of radius 4 cm have angles 90° and 60°. What is their combined area?

    • 16π cm²
    • 10π cm²
    • 25π/3 cm²
    • 20π/3 cm²

18. An arc of length 8π cm is on a circle of radius 12 cm. What is the sector's angle?

    • 30°
    • 240°
    • 120°
    • 60°

19. A pendulum of radius 30 cm swings through an arc length of 5π cm. What is the angle of the swing?

    • 15°
    • 30°
    • 60°
    • 45°

20. A sector has radius 5 cm and angle 216°. What is its area in terms of π?

    • 45π cm²
    • 30π cm²
    • 15π cm²
    • 9π cm²

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