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0580/42 Feb/Mar 2021, Question 10: Compound Measures

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 11 marks

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The question, in short

Work with sand volumes, density, percentage used, tax and currency conversion across four parts.

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

Part (a) · 3 marks

Find the density in kg/m³ of sand filling a 45 cm by 30 cm by 42 cm cuboid box holding 90.72 kg.

  1. 1Volume = 0.45 × 0.30 × 0.42 = 0.0567 m³
  2. 2Density = 90.72 ÷ 0.0567
  3. 3= 1600 kg/m³

Answer1600

Part (b) · 3 marks

Find the percentage of 15000 cm³ bag sand used to fill a 30 cm deep cylinder of radius 10 cm.

  1. 1Volume of hole = π × 10² × 30 = 9424.7… cm³
  2. 2Percentage = 9424.7… ÷ 15 000 × 100
  3. 3= 62.83… ≈ 62.8%

Answer62.8 or 62.83 to 62.84

Part (c) · 3 marks

Find the tax amount per tonne when sand costs $98.90 per tonne including 15% tax.

  1. 198.90 is 115% of the price before tax
  2. 2Price before tax = 98.90 ÷ 1.15 = 86
  3. 3Tax = 98.90 − 86 = $12.90

Answer12.90

Part (d) · 2 marks

Convert 3540 rupees to dollars at the rate $1 = 70.8 rupees.

  1. 13540 ÷ 70.8 = $50

Answer50

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