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0580/33 Oct/Nov 2021, Question 5: Nets of 3D Shapes

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 12 marks

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The question, in short

Work with a 4 cm by 2 cm by 2 cm cuboid: draw its net, find its surface area, estimate faulty ones from a sample, then handle a cube and a rounded length.

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, complete an accurate net of the cuboid, using the given 4 cm by 2 cm face.

  1. 1Faces needed: four 4 × 2 rectangles and two 2 × 2 squares
  2. 2Attach three more 4 × 2 rectangles in a strip below the given face
  3. 3Attach a 2 × 2 square to each short end of one rectangle in the strip

AnswerFully correct net: four 4 cm by 2 cm rectangles and two 2 cm by 2 cm squares joined correctly to the given face

Part (aii) · 2 marks

Calculate the total surface area of the 4 cm by 2 cm by 2 cm cuboid.

  1. 14 faces of 4 × 2 = 32
  2. 22 faces of 2 × 2 = 8
  3. 3Surface area = 40 cm²

Answer40

Part (aiii) · 2 marks

From 25 checked cuboids with 3 faulty, estimate how many of 5000 would be faulty.

  1. 1Relative frequency faulty = 3/25
  2. 23/25 × 5000 = 600

Answer600

Part (b) · 3 marks

A cube has surface area 294 cm²; calculate its volume.

  1. 1One face = 294 ÷ 6 = 49 cm²
  2. 2Edge = √49 = 7 cm
  3. 3Volume = 7³ = 343 cm³

Answer343

Part (c) · 2 marks

The length l is 24 cm to the nearest centimetre; complete the inequality for l.

  1. 1Nearest cm: 0.5 either side
  2. 2Lower bound 23.5, upper bound 24.5

Answer23.5 ≤ l < 24.5

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Also searched as: 0580/33/O/N/21 · 0580_w21_qp_33 · 0580 w21 33 · question 5.
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