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0580/43 May/Jun 2024, Question 8: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 14 marks

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The question, in short

Work with a composite solid formed from a cylinder and a cone, each with radius 0.35 cm, cylinder height 16 cm and cone height 1.5 cm, then compare two similar solids.

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

Part (ai) · 5 marks

Find the total surface area of the cylinder-and-cone solid, using the cone curved surface formula A = πrl.

  1. 1Slant height l = √(0.35² + 1.5²) = 1.540…
  2. 2Cone curved surface = π × 0.35 × 1.540… = 1.693…
  3. 3Cylinder curved surface = 2 × π × 0.35 × 16 = 35.185…
  4. 4Circular end = π × 0.35² = 0.3848…
  5. 5Total = 1.693… + 35.185… + 0.3848… = 37.3 cm²

Answer37.3 or 37.26 to 37.27

Part (aii) · 3 marks

Find the volume of the cylinder-and-cone solid, using the cone volume formula V = 1/3πr²h.

  1. 1Cylinder = π × 0.35² × 16 = 6.157…
  2. 2Cone = 1/3 × π × 0.35² × 1.5 = 0.1924…
  3. 3Total = 6.35 cm³

Answer6.35 or 6.349 to 6.351

Part (aiii) · 3 marks

Ten solids fill a cuboid box of length 17.5 cm; from the end view, find the unoccupied volume inside the box.

  1. 1Box volume = 17.5 × 3.5 × 1.4 = 85.75 cm³
  2. 210 solids = 10 × 6.349… = 63.49… cm³
  3. 3Empty space = 85.75 − 63.49… = 22.25 cm³

Answer22.2 or 22.3 or 22.24 to 22.26

Part (b) · 3 marks

Two similar solids have surface areas 200 cm² and 98 cm²; the larger volume is 450 cm³, so find the smaller volume.

  1. 1Area factor = 98/200 = 0.49
  2. 2Length factor = √0.49 = 0.7
  3. 3Volume factor = 0.7³ = 0.343
  4. 4Volume = 450 × 0.343 = 154 cm³

Answer154 or 154.3 to 154.4

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