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4024/22 Oct/Nov 2024, Question 3: Composite Perimeter, Area and Volume

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 10 marks

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The question, in short

Work with a cuboid tank of length 1.2 m, width 0.6 m and volume 1.8 m³, then an open-top trapezium prism tank with AD = BC = 70 cm, CD = 80 cm, AB = 110 cm and a square base.

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

Part (ai) · 2 marks

Find the height h of the cuboid tank using its length, width and volume.

  1. 11.2 × 0.6 × h = 1.8
  2. 20.72h = 1.8, h = 2.5

Answer2.5

Part (aii) · 3 marks

Fuel enters at 0.2 m³ per minute; work out how long until the tank is 90% full, in minutes and seconds.

  1. 190% of 1.8 = 1.62 m³
  2. 2Time = 1.62 ÷ 0.2 = 8.1 minutes
  3. 30.1 × 60 = 6 seconds, so 8 minutes 6 seconds

Answer8 minutes 6 seconds

Part (b) · 5 marks

For the open-top prism tank, work out the total area of its outer surfaces.

  1. 1Height of trapezium = √(70² − 15²) = √4675 = 68.37… cm (overhang (110 − 80)/2 = 15)
  2. 2Trapezium area = 1/2 × (110 + 80) × 68.37… = 6495.5… cm²
  3. 3Base is square: 80 × 80 = 6400 cm²; two sloping sides: 2 × 80 × 70 = 11 200 cm²
  4. 4Total = 2 × 6495.5… + 6400 + 11 200
  5. 5= 30 591.0… ≈ 30 600 cm²

Answer30 600 or 30 590 to 30 591…

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Also searched as: 4024/22/O/N/24 · 4024_w24_qp_22 · 4024 w24 22 · question 3.
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