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0580/33 May/Jun 2021, Question 3: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 12 marks

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The question, in short

Use scale drawings and measurements to find a garden's real area, a gate diagonal length, and the cost of grass seed for a garden with a quarter-circle patio.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 3 marks

Measure the rectangle on the scale drawing and convert using 1 cm represents 8 m to find the actual garden area.

  1. 1Measured rectangle: 6 cm by 10 cm
  2. 2Actual size: 6 × 8 = 48 m and 10 × 8 = 80 m
  3. 3Area = 48 × 80 = 3840 m²

Answer3840 or 3637.76 to 4047.36

Part (b) · 3 marks

In rectangle FGHJ with GJ = 2.1 m and FG = 0.85 m, find the length FJ.

  1. 1Triangle FGJ has a right angle at F: GJ² = FG² + FJ²
  2. 2FJ² = 2.1² − 0.85² = 4.41 − 0.7225 = 3.6875
  3. 3FJ = √3.6875 = 1.920… ≈ 1.92 m

Answer1.92 or 1.920…

Part (c) · 6 marks

For an 85 m by 24 m garden with a quarter-circle patio of radius 24 m, find the grass seed cost at 40 g/m², 1 kg bags costing $6.80.

  1. 1Rectangle = 85 × 24 = 2040 m²
  2. 2Patio = π × 24² ÷ 4 = 452.38… m²
  3. 3Grass = 2040 − 452.38… = 1587.6… m²
  4. 4Seed = 1587.6… × 40 ÷ 1000 = 63.5… kg, so buy 64 bags
  5. 5Cost = 64 × 6.80 = $435.20

Answer435.20

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