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0580/31 Oct/Nov 2022, Question 3: Surface Area of a Cuboid and Cylinder

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

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The question, in short

Work through Miguel's office scenario: find his arrival time from a 07 45 start and 40 minute journey, show the 38 km distance at 57 km/h, form a cost expression in w and p, get the surface area of a 20 cm by 12 cm by 7 cm cuboid, then handle grouped call-time data.

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

Part (ai) · 1 mark

Given a 40 minute journey starting at 07 45, work out when he gets to work.

  1. 107 45 + 15 minutes = 08 00
  2. 208 00 + 25 minutes = 08 25

Answer08 25

Part (aii) · 2 marks

Using 57 km/h and 40 minutes, demonstrate that the journey covers 38 km.

  1. 140 minutes = 40/60 hours
  2. 2Distance = 57 × 40/60
  3. 3= 38 km

Answer57 × 40/60 [= 38]

Part (b) · 2 marks

With white sheets at w cents and pink at p cents, write the total cost in cents for 56 white and 21 pink sheets.

  1. 1White paper cost = 56 × w = 56w
  2. 2Pink paper cost = 21 × p = 21p
  3. 3Total = 56w + 21p

Answer56w + 21p

Part (c) · 3 marks

For a closed cuboid box measuring 20 cm, 12 cm and 7 cm, work out its surface area.

  1. 1Faces: 20 × 12 = 240, 20 × 7 = 140, 12 × 7 = 84
  2. 2Surface area = 2(240 + 140 + 84)
  3. 3= 2 × 464 = 928 cm²

Answer928

Part (di) · 2 marks

Sort the twenty recorded call lengths into the six given time classes and give each class frequency.

  1. 10 − 5: 3, 4 → 2
  2. 26 − 10: 7, 6, 8, 9 → 4
  3. 311 − 15: 15, 12, 11, 12, 14 → 5
  4. 416 − 20: 17, 19, 20, 19, 20, 18 → 6
  5. 521 − 25: 21, 23 → 2; 26 − 30: 28 → 1

Answer2, 4, 5, 6, 2, 1

Part (dii) · 3 marks

Plot the frequencies as bars on the grid, first choosing and completing a suitable scale on the frequency axis.

  1. 1Label the frequency axis 0, 1, 2, … up to at least 6 (one unit per grid line)
  2. 2Draw bars of equal width for each group
  3. 3Heights: 2, 4, 5, 6, 2, 1

AnswerSuitable scale on frequency axis; bars at heights 2, 4, 5, 6, 2, 1; bars of equal width

Part (diii) · 1 mark

From your bar chart, state which time group occurs most often.

  1. 1The tallest bar is 16 − 20 (frequency 6)
  2. 2Modal group = 16 − 20

Answer16 to 20

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Also searched as: 0580/31/O/N/22 · 0580_w22_qp_31 · 0580 w22 31 · question 3.
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