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Year 11 Maths — Areas related to circles

Find the arc length, area and perimeter of a sector, and the area of a segment.

Name: ________________________

  1. 1.A sector of a circle of radius 7 cm has an angle of 90° at the centre. Take π = 22/7. How long is its arc, in centimetres?

  2. 2.A sector of a circle of radius 21 cm has an angle of 60° at the centre. Take π = 22/7. How long is its arc, in centimetres?

  3. 3.Doubling a sector's radius while keeping its angle at the centre the same multiplies its area by what?

    • a) 2
    • b) 4
    • c) 3
    • d) 8

  4. 4.A sector of a circle of radius 6 cm has an angle of 60° at the centre. Take π = 3.14. What is its area, in square centimetres?

  5. 5.A quadrant is a sector with an angle of 90° at the centre. Take π = 22/7. What is the area of a quadrant of a circle of radius 14 cm, in square centimetres?

  6. 6.A sector of a circle of radius 21 cm has an angle of 60° at the centre. Take π = 22/7. What is its area, in square centimetres?

  7. 7.A circle has been cut into three sectors. Tap the sector with the largest area.

    Write the number of the part.

    123

  8. 8.Match each sector to its area, in square centimetres. Take π = 22/7.

    • radius 7 cm, angle 45°
    • radius 7 cm, angle 135°
    • radius 14 cm, angle 180°
    • radius 21 cm, angle 45°
    • 19.25
    • 173.25
    • 308
    • 57.75

Answer key — Year 11 Maths — Areas related to circles

  1. 1. 11
  2. 2. 22
  3. 3. b) 4
  4. 4. 18.84
  5. 5. 154
  6. 6. 231
  7. 7. 3 — Sector C
  8. 8. radius 7 cm, angle 45° → 19.25; radius 7 cm, angle 135° → 57.75; radius 14 cm, angle 180° → 308; radius 21 cm, angle 45° → 173.25