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0580/43 May/Jun 2023, Question 3: Volume Factor of Similar Shapes

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 10 marks

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The question, in short

Use a 5 cm to 200 m scale drawing of field sides AB and BC; measure angle ABC, locate X on BC with BX = 332 m, express the scale as 1 : n, and find the height of a similar model statue.

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

Part (ai) · 1 mark

Measure angle ABC on the scale drawing.

  1. 1Place the protractor's centre on B with the baseline along BC
  2. 2Read the angle up to BA: 118°

Answer118° (accept 116 to 120)

Part (aii) · 2 marks

Mark point X on BC where BX = 332 m, using the scale.

  1. 1332 ÷ 200 × 5 = 8.3 cm
  2. 2Measure 8.3 cm from B along BC and mark X

AnswerX marked on BC, 8.3 cm from B

Part (aiii) · 2 marks

Give the drawing scale in the form 1 : n.

  1. 15 cm represents 200 m = 20 000 cm
  2. 21 cm represents 20 000 ÷ 5 = 4000 cm
  3. 3Scale 1 : 4000

Answer1 : 4000

Part (b) · 5 marks

Given the statue's height, mass, bronze density and model volume, calculate the model's height.

  1. 1Volume of statue = 195 200 ÷ 8000 = 24.4 m³
  2. 2Volume scale factor = 0.385 ÷ 24.4 = 0.01578…
  3. 3Length scale factor = ∛0.01578… = 0.2508…
  4. 4Height = 4.5 × 0.2508… = 1.128… ≈ 1.13 m

Answer1.13 or 1.128 to 1.129

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Also searched as: 0580/43/M/J/23 · 0580_s23_qp_43 · 0580 s23 43 · question 3.
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