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0580/32 Feb/Mar 2022, Question 5: Nets of 3D Shapes

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 13 marks

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The question, in short

A cuboid box measures 5 cm by 4 cm by 2 cm; use a 1 cm² grid for its net, pack such boxes into a 1 m³ cube container, compare three rice boxes sold at equal cost per kilogram, and convert 75 cm³ to litres.

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

Part (ai) · 3 marks

On the 1 cm² grid, produce a flat unfolded pattern for the 5 cm by 4 cm by 2 cm cuboid box.

  1. 1Draw the base as a 5 cm by 4 cm rectangle
  2. 2Attach 5 × 2 rectangles to both 5 cm edges and 4 × 2 rectangles to both 4 cm edges
  3. 3Attach the 5 × 4 lid to the far edge of one 5 × 2 rectangle

AnswerCorrect ruled net: two 5 × 4, two 5 × 2 and two 4 × 2 rectangles in correct positions

Part (aii) · 3 marks

Determine how many of the 5 cm by 4 cm by 2 cm boxes fit at most inside a cube container holding 1 m³.

  1. 11 m = 100 cm
  2. 2100 ÷ 5 = 20, 100 ÷ 4 = 25, 100 ÷ 2 = 50
  3. 320 × 25 × 50 = 25 000

Answer25 000

Part (bi) · 2 marks

Given box A holds 750 g for 80 rupees and box B holds 1.35 kg, find box B's price in rupees at the same rate per kilogram.

  1. 11.35 kg = 1350 g
  2. 21350 ÷ 750 = 1.8
  3. 31.8 × 80 = 144 rupees

Answer144

Part (bii) · 3 marks

Using $1 = 64 rupees and box C costing $3.50, find box C's mass in kilograms at the shared cost per kilogram.

  1. 1$3.50 = 3.5 × 64 = 224 rupees
  2. 2224 ÷ 80 = 2.8
  3. 32.8 × 0.75 = 2.1 kg

Answer2.1

Part (c) · 2 marks

Express 75 cm³ as a volume in litres, writing the result in standard form.

  1. 11 litre = 1000 cm³
  2. 275 ÷ 1000 = 0.075
  3. 30.075 = 7.5 × 10⁻²

Answer7.5 × 10⁻²

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Also searched as: 0580/32/F/M/22 · 0580_m22_qp_32 · 0580 m22 32 · question 5.
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