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0580/31 Oct/Nov 2024, Question 7: Pythagoras' Theorem

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 11 marks

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The question, in short

Work through four measurement questions: triangle perimeter, area of a T-shape, area of a right-angled triangle, and volume of a sphere with diameter 5.25 cm.

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

Part (a) · 1 mark

Find the perimeter of a triangle with sides 4 cm, 7 cm and 10 cm.

  1. 14 + 7 + 10 = 21 cm

Answer21

Part (b) · 3 marks

Calculate the area of a T-shape built from rectangles, using top width 18.6 cm, bar height 4 cm, total height 13.5 cm and 7 cm overhangs.

  1. 1Top bar: 18.6 × 4 = 74.4 cm²
  2. 2Stem width = 18.6 − 7 − 7 = 4.6 cm, stem height = 13.5 − 4 = 9.5 cm
  3. 3Stem: 4.6 × 9.5 = 43.7 cm²
  4. 4Area = 74.4 + 43.7 = 118.1 cm²

Answer118.1

Part (c) · 5 marks

Calculate the area of right-angled triangle ABC with right angle at A, AC = 24 cm and BC = 27.2 cm.

  1. 1AB² + 24² = 27.2²
  2. 2AB = √(27.2² − 24²) = √(739.84 − 576) = √163.84 = 12.8 cm
  3. 3Area = 1/2 × 24 × 12.8 = 153.6 cm²

Answer153.6

Part (d) · 2 marks

Calculate the volume of a sphere of diameter 5.25 cm using V = 4/3 πr³.

  1. 1r = 5.25 ÷ 2 = 2.625 cm
  2. 2V = 4/3 × π × 2.625³
  3. 3= 75.766… ≈ 75.8 cm³

Answer75.8 or 75.76 to 75.78

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Also searched as: 0580/31/O/N/24 · 0580_w24_qp_31 · 0580 w24 31 · question 7.
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