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0580/32 Oct/Nov 2024, Question 4: Pythagoras' Theorem

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

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The question, in short

Work through five measurement problems: cylinder volume, cube surface area from volume, comparing two areas in different units, a right-angled triangle angle, and a rectangle area from a diagonal.

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

Part (a) · 2 marks

Find the volume of a cylinder having radius 7.8 cm and height 15 cm.

  1. 1V = πr²h
  2. 2= π × 7.8² × 15
  3. 3= 2867.0… ≈ 2870 cm³

Answer2870 or 2867 to 2867.4

Part (b) · 3 marks

Given a cube's volume is 3375 cm³, work out its total surface area.

  1. 1Side = ∛3375 = 15 cm
  2. 2Area of one face = 15² = 225 cm²
  3. 3Surface area = 6 × 225 = 1350 cm²

Answer1350

Part (c) · 2 marks

Decide which is bigger, 37 000 cm² or 5.4 m², showing all working.

  1. 11 m² = 100² cm² = 10 000 cm²
  2. 25.4 m² = 5.4 × 10 000 = 54 000 cm²
  3. 354 000 > 37 000, so Area B is larger

AnswerArea B

Part (d) · 2 marks

In right-angled triangle ABC with right angle at B, AB = 7 cm and AC = 15 cm; find angle ACB.

  1. 1sin ACB = opp/hyp = 7/15
  2. 2ACB = sin⁻¹(7/15)
  3. 3= 27.8°

Answer27.8 or 27.81… to 27.82

Part (e) · 4 marks

Rectangle DEFG has DE = 12 cm and diagonal DF = 31.2 cm; work out its area.

  1. 1EF² = 31.2² − 12²
  2. 2= 973.44 − 144 = 829.44
  3. 3EF = √829.44 = 28.8 cm
  4. 4Area = 28.8 × 12 = 345.6 cm²

Answer345.6

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Also searched as: 0580/32/O/N/24 · 0580_w24_qp_32 · 0580 w24 32 · question 4.
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