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0580/42 Oct/Nov 2023, Question 4: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 12 marks

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The question, in short

Use sector-to-cone and sphere/cylinder/cube diagrams to find a sector angle, verify a cylinder height, compare volumes, and find a new water depth.

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

Part (a) · 3 marks

Sector radius 7.5 cm becomes cone slant height; base radius 1.5 cm. Find sector angle x.

  1. 1Arc length = circumference of base: x/360 × 2π × 7.5 = 2π × 1.5
  2. 2x = 360 × 1.5/7.5
  3. 3x = 72

Answer72 or 72.0

Part (bi) · 2 marks

Cylinder radius 8 cm in sphere radius 17 cm, ends touching sphere. Show cylinder height is 30 cm.

  1. 1Half the height: d² + 8² = 17², d = √(289 − 64) = √225 = 15
  2. 2Height = 2 × 15 = 30 cm

Answer2 × √(17² − 8²) or √(34² − 16²)

Part (bii) · 4 marks

Find cylinder volume as a percentage of sphere volume, using V = 4/3 πr³.

  1. 1Half the cylinder height = √(17² − 8²) = √225 = 15 cm, so height = 30 cm.
  2. 2Cylinder volume = π × 8² × 30 = 1920π
  3. 3Sphere volume = 4/3 × π × 17³ = 6550.66…π
  4. 41920π ÷ 6550.66…π × 100 = 29.30…% ≈ 29.3

Answer29.3 or 29.30 to 29.31

Part (c) · 3 marks

Sphere radius 6 cm removed from cube side 20 cm with water depth 15 cm. Find new water depth.

  1. 1Sphere volume = 4/3 × π × 6³ = 904.77… cm³
  2. 2Fall in depth = 904.77… ÷ 20² = 2.2619… cm
  3. 3New depth = 15 − 2.2619… = 12.738… ≈ 12.7 cm

Answer12.7 or 12.73 to 12.74

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Also searched as: 0580/42/O/N/23 · 0580_w23_qp_42 · 0580 w23 42 · question 4.
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