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0580/32 May/Jun 2022, Question 1: Volume and Surface Area of a Sphere

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 17 marks

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The question, in short

Antonio's shop: tally ice creams, fraction vanilla, ratio of tubs, chair statistics, beach ball profit and volume, and best-value sun cream bottle.

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

Part (ai) · 1 mark

Count the tally marks to find how many ice creams were sold on Friday.

  1. 19 groups of 5 and 3 more: 9 × 5 + 3
  2. 2= 48

Answer48

Part (aii) · 1 mark

Given 15 vanilla, express vanilla sales as a fraction of Friday's total in simplest form.

  1. 115/48 = 5/16

Answer5/16

Part (aiii) · 2 marks

Using vanilla:chocolate = 11:7 and 28 chocolate tubs, find the number of vanilla tubs.

  1. 17 parts = 28 tubs, so 1 part = 4
  2. 2Vanilla = 11 × 4 = 44

Answer44

Part (bi) · 1 mark

Find the range of the seven daily chair-hire numbers.

  1. 1Range = 165 − 45 = 120

Answer120

Part (bii) · 2 marks

Find the median of the seven daily chair-hire numbers.

  1. 1In order: 45, 67, 98, 116, 123, 156, 165
  2. 2Median = 4th value = 116

Answer116

Part (biii) · 2 marks

Calculate the mean number of chairs hired per day over the week.

  1. 1Sum = 123 + 98 + 116 + 45 + 67 + 165 + 156 = 770
  2. 2Mean = 770 ÷ 7 = 110

Answer110

Part (ci) · 2 marks

With cost $2.50 and selling price $4.20, find the percentage profit per beach ball.

  1. 1Profit = 4.20 − 2.50 = 1.70
  2. 2Percentage profit = 1.70 ÷ 2.50 × 100 = 68%

Answer68

Part (cii) · 3 marks

For a sphere of radius 15 cm, calculate its volume using V = 4/3 πr³, with units.

  1. 1V = 4/3 × π × 15³ = 4500π
  2. 2= 14137.1… ≈ 14100 cm³

Answer14100 or 14140 or 14137 to 14139 cm³

Part (d) · 3 marks

Compare cost per ml for bottles A (160 ml, $3.75), B (200 ml, $4.75), C (240 ml, $6.50) and state the best value.

  1. 1A: 160 ÷ 3.75 = 42.7 ml per $
  2. 2B: 200 ÷ 4.75 = 42.1 ml per $
  3. 3C: 240 ÷ 6.50 = 36.9 ml per $
  4. 4Most ml per dollar: bottle A

AnswerA

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Also searched as: 0580/32/M/J/22 · 0580_s22_qp_32 · 0580 s22 32 · question 1.
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