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0580/31 May/Jun 2022, Question 4: Nets of 3D Shapes

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 13 marks

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The question, in short

Complete a net of a right-angled triangular prism with legs 4 cm and 3 cm and length 7 cm, then find its volume; for a rectangle holding 6 circles of radius 8 cm, show the length, find the rectangle area, and find the shaded percentage.

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

Part (ai) · 4 marks

On the 1 cm² grid, complete the net of the prism, using the given 7 cm by 3 cm rectangle as one face.

  1. 1The end triangle has sides 3 cm, 4 cm and hypotenuse 5 cm (3-4-5 triangle)
  2. 2Draw a 7 cm by 4 cm rectangle and a 7 cm by 5 cm rectangle joined along the 7 cm edges next to the 3 cm by 7 cm face
  3. 3Draw the two right-angled triangles (3 cm and 4 cm sides) on the ends, sharing edges with the rectangles

AnswerFully correct net

Part (aii) · 2 marks

Work out the volume of the right-angled triangular prism.

  1. 1Volume = area of triangle × length = 1/2 × 4 × 3 × 7
  2. 2= 42 cm³

Answer42

Part (bi) · 1 mark

Show that the rectangle's length is 48 cm using the 8 cm circle radius and the arrangement.

  1. 1Three circles fit along the length, each 2 × 8 = 16 cm wide
  2. 2Length = 2 × 8 × 3 = 48 cm

Answer2 × 8 × 3 or 16 + 16 + 16 or 16 × 3 or 8 × 6 or 8 + 8 + 8 + 8 + 8 + 8

Part (bii) · 3 marks

Find the area of the rectangle, giving the units.

  1. 1Width = two diameters = 2 × 16 = 32 cm
  2. 2Area = 32 × 48
  3. 3= 1536 cm²

Answer1536 cm²

Part (biii) · 3 marks

Calculate the percentage of the rectangle's area that is shaded.

  1. 1Circles = 6 × π × 8² = 1206.3…
  2. 2Shaded = 1536 − 1206.3… = 329.6…
  3. 3Percentage = 329.6… ÷ 1536 × 100 = 21.46… ≈ 21.5%

Answer21.5 or 21.45 to 21.47

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Also searched as: 0580/31/M/J/22 · 0580_s22_qp_31 · 0580 s22 31 · question 4.
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