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0580/43 Oct/Nov 2024, Question 4: Volume of a Prism

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 15 marks

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The question, in short

Answer six parts on mass, volume, density and cone surface area: find box mass in grams, water volume, prism mass, show cone area 1131 cm², cost per cm² in cents, and cones per tin.

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

Part (a) · 2 marks

Total mass is 7 kg with 50 cuboids each 135 g; find the box mass in grams.

  1. 1Cuboids = 50 × 135 = 6750 g
  2. 2Box = 7000 − 6750 = 250 g

Answer250

Part (b) · 2 marks

A 4 cm cube sits on the base of a 6 cm cube; find the water volume needed to reach the small cube's top.

  1. 1Volume up to 4 cm = 6 × 6 × 4 = 144 cm³
  2. 2Small cube = 4³ = 64 cm³
  3. 3Water = 144 − 64 = 80 cm³

Answer80

Part (c) · 4 marks

Equilateral triangular prism, side 4 cm, length 20 cm, wood density 0.85 g/cm³; find its mass.

  1. 1Area of triangle = 1/2 × 4 × 4 × sin60° = 6.928... cm²
  2. 2Volume = 6.928... × 20 = 138.56... cm³
  3. 3Mass = 0.85 × 138.56... = 117.8 g
  4. 4= 118 g

Answer118 or 117.7 to 117.8

Part (di) · 4 marks

Cone radius 10 cm, height 24 cm; find slant height and show total surface area rounds to 1131 cm².

  1. 1Slant height l = √(24² + 10²) = √676 = 26 cm
  2. 2Curved area = π × 10 × 26 = 816.81... cm²
  3. 3Base area = π × 10² = 314.15... cm²
  4. 4Total = 1130.97... = 1131 cm² to the nearest cm²

Answerπ × 10 × √(24² + 10²) + π × 10² = 1130.9 to 1131.1..., so 1131

Part (diia) · 1 mark

Painting the cone costs $1.71; find the cost per cm² in cents.

  1. 1$1.71 = 171 cents
  2. 2171 ÷ 1130.97... = 0.151 cents

Answer0.151 or 0.1511 to 0.1512...

Part (diib) · 2 marks

One tin covers 2.5 m²; find how many complete cones can be painted with one tin.

  1. 12.5 m² = 2.5 × 100² = 25000 cm²
  2. 225000 ÷ 1131 = 22.1...
  3. 322 cones can be painted completely

Answer22

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Also searched as: 0580/43/O/N/24 · 0580_w24_qp_43 · 0580 w24 43 · question 4.
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