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4MA1/2H Jan 2021, Question 17: Surface Area of a Cuboid and Cylinder

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 7 marks

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The question, in short

For a prism with trapezium cross-section ABCD, parallel sides AD = 37 cm and BC = 28 cm, height 20 cm, and length DE = 24 cm, find the total surface area and the angle between AF and the horizontal base.

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

Part (a) · 4 marks

Find the total surface area of the prism using the trapezium cross-section and rectangular faces.

  1. 1Trapezium area = (37 + 28)/2 × 20 = 650, so the two ends = 1300
  2. 2Slant edge AB = √(4.5² + 20²) = 20.5, since (37 − 28) ÷ 2 = 4.5
  3. 3Rectangles: 2 × 20.5 × 24 = 984, 37 × 24 = 888, 28 × 24 = 672
  4. 4Total = 1300 + 984 + 888 + 672 = 3844

Answer3844

Part (b) · 3 marks

Find the angle between the line AF and the horizontal plane ADEH, to one decimal place.

  1. 1F is above a point 37 − 4.5 = 32.5 cm along and 24 cm across from A
  2. 2Distance on the base = √(32.5² + 24²) = 40.4… cm
  3. 3tan θ = 20 ÷ 40.4…
  4. 4θ = 26.3°

Answer26.3

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