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4024/21 May/Jun 2020, Question 8: Area of a Sector

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

For a display notice formed from two 110° sectors with radii 80 cm and 45 cm, find the outer arc length L and the shaded area; then use similarity with larger radius 32 cm to find the area.

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Part (ai) · 2 marks

Calculate the length L of the outer arc of the 110° sector with radius 80 cm.

  1. 1L = 110/360 × 2 × π × 80
  2. 2= 153.58… ≈ 154 cm

Answer154 or 153.5 to 153.6

Part (aii) · 3 marks

Calculate the area of the shaded display notice using radii 80 cm and 45 cm with angle 110°.

  1. 1Area = 110/360 × π × (80² − 45²)
  2. 2= 110/360 × π × 4375
  3. 3= 4199.7 ≈ 4200 cm²

Answer4199 to 4200…

Part (b) · 2 marks

Using the mathematically similar notice with larger radius 32 cm, calculate its area.

  1. 1Length scale factor = 32/80 = 0.4
  2. 2Area scale factor = 0.4² = 0.16
  3. 3Area = 4199.7 × 0.16 = 671.95… ≈ 672 cm²

Answer671.8 to 672.0…

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