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0580/42 May/Jun 2024, Question 9: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 10 marks

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The question, in short

Find a and b for the perimeter of shaded shape ABDC, formed by two sectors with radii 17 cm and 10 cm and angle 60°. Then work with a regular hexagon of area 127.3 cm² and a prism of length 10 cm.

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

Part (a) · 3 marks

Perimeter of shaded region ABDC between arcs of sectors radius 17 cm and 10 cm, angle 60°, written as aπ + b; find a and b.

  1. 1Arc AB = 60/360 × 2 × π × 17 = 17π/3
  2. 2Arc CD = 60/360 × 2 × π × 10 = 10π/3
  3. 3Straight edges: CA + DB = 7 + 7 = 14
  4. 4Perimeter = 27π/3 + 14 = 9π + 14
  5. 5a = 9, b = 14

Answera = 9, b = 14

Part (bi) · 4 marks

Show that a regular hexagon of area 127.3 cm² has side length 7.0 cm to 1 decimal place.

  1. 1Hexagon = 6 equilateral triangles of side s
  2. 26 × 1/2 × s² × sin 60 = 127.3
  3. 3s² = 127.3 ÷ (3 × sin 60) = 48.99…
  4. 4s = 6.999… = 7.0 cm (1 d.p.)

Answer6.999… to 7.00…

Part (biia) · 1 mark

Find the volume of a prism with hexagonal cross-section area 127.3 cm² and length 10 cm.

  1. 1Volume = 127.3 × 10 = 1273 cm³

Answer1273

Part (biib) · 2 marks

Calculate the total surface area of the hexagonal prism with side 7.0 cm and length 10 cm.

  1. 1Two hexagons: 2 × 127.3 = 254.6
  2. 2Six rectangles: 6 × 7 × 10 = 420
  3. 3Surface area = 254.6 + 420 = 674.6 ≈ 675 cm²

Answer675 or 674.5 to 674.6

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