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0580/43 Oct/Nov 2021, Question 3: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 17 marks

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The question, in short

Work with a trapezium-section prism of volume 525 cm³, AB = 10 cm, CD = 4 cm, height 5 cm, made of iron at 7.8 g per cm³; also handle a 10 cm by 4 cm by 6 cm cuboid with rounded measurements.

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

Part (ai) · 2 marks

Using 7.8 g per cm³, work out the iron prism's mass and express it in kilograms.

  1. 1Mass = 525 × 7.8 = 4095 g
  2. 2= 4095 ÷ 1000 = 4.095 kg

Answer4.095

Part (aii) · 3 marks

Given the 525 cm³ volume and the trapezium cross-section, work out how long the prism is.

  1. 1Cross-section area = 1/2 × (10 + 4) × 5 = 35 cm²
  2. 2Length = 525 ÷ 35 = 15 cm

Answer15

Part (aiii) · 6 marks

Work out the prism's total surface area, including both trapezium ends and all rectangular faces.

  1. 1Trapezium area = 1/2 × (10 + 4) × 5 = 35 cm², so length = 525 ÷ 35 = 15 cm
  2. 2Sloping sides: AC = BD = √(3² + 5²) = √34 = 5.830… cm
  3. 3Two ends = 2 × 35 = 70; rectangles 15 × 10 = 150 and 15 × 4 = 60
  4. 4Two sloping rectangles = 2 × 15 × 5.830… = 174.93…
  5. 5Total = 70 + 150 + 60 + 174.93… = 454.9… ≈ 455 cm²

Answer455 or 454.9...

Part (aiv) · 3 marks

For a similar prism whose trapezium height is 10 cm, work out its volume.

  1. 1Length scale factor = 10/5 = 2, volume factor = 2³ = 8
  2. 2Volume = 525 × 8 = 4200 cm³

Answer4200

Part (b) · 3 marks

With each side of the 10 cm by 4 cm by 6 cm cuboid rounded to the nearest cm, fill in the lower and upper bounds for V.

  1. 1Bounds: 9.5 to 10.5, 3.5 to 4.5, 5.5 to 6.5
  2. 2Lower = 9.5 × 3.5 × 5.5 = 182.875
  3. 3Upper = 10.5 × 4.5 × 6.5 = 307.125
  4. 4182.875 ≤ V < 307.125

Answer182.875 ≤ V < 307.125

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Also searched as: 0580/43/O/N/21 · 0580_w21_qp_43 · 0580 w21 43 · question 3.
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