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0580/31 Oct/Nov 2021, Question 7: Volume of a Prism

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 14 marks

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The question, in short

Use a cuboid net on a 1 cm² grid and a cylinder of radius 3.2 cm and volume 775 cm³ to work out folded corners, an edge match, surface area, volume, L, a sphere's volume and empty percentage.

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

Part (aia) · 1 mark

State the two corners that meet corner A when the net is folded into a cuboid.

  1. 1When folded, edge AB meets edge CB and edge AN meets edge GH
  2. 2So C and G join to A

AnswerC and G

Part (aib) · 1 mark

State which edge of the net coincides with edge KL on folding.

  1. 1KL is the end of flap JKLM; it folds to meet the edge HI

AnswerHI

Part (aii) · 2 marks

Work out the cuboid's total surface area from the grid net.

  1. 1The cuboid is 5 cm × 4 cm × 2 cm
  2. 2Area = 2(5 × 4 + 5 × 2 + 4 × 2) = 2(20 + 10 + 8)
  3. 3= 76 cm²

Answer76

Part (aiii) · 2 marks

Work out the cuboid's volume from the grid net.

  1. 1Volume = 5 × 2 × 4 = 40 cm³

Answer40

Part (bi) · 3 marks

Given radius 3.2 cm and volume 775 cm³, work out the cylinder length L.

  1. 1775 = π × 3.2² × L
  2. 2L = 775 ÷ (π × 3.2²) = 775 ÷ 32.17…
  3. 3L = 24.09… ≈ 24.1

Answer24.1 or 24.08 to 24.09…

Part (bii) · 2 marks

Work out the volume of a sphere of radius 3 cm using V = 4/3 πr³.

  1. 1V = 4/3 × π × 3³
  2. 2= 113.09… ≈ 113 cm³

Answer113 or 113.09 to 113.11…

Part (biii) · 3 marks

With four 3 cm spheres inside the cylinder, work out the percentage of the cylinder left empty.

  1. 1Volume of one sphere (radius 3 cm) = 4/3 × π × 3³ = 113.09… cm³
  2. 2Volume of 4 spheres = 4 × 113.09… = 452.38… cm³
  3. 3Empty space = 775 − 452.38… = 322.61… cm³
  4. 4Percentage empty = 322.61… ÷ 775 × 100 = 41.6

Answer41.6 to 41.7

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Also searched as: 0580/31/O/N/21 · 0580_w21_qp_31 · 0580 w21 31 · question 7.
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