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0580/43 May/Jun 2021, Question 8: Area of a Sector

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 15 marks

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The question, in short

Work with a 20 cm by 12 cm by 5 cm cuboid, then a cylinder of radius x and height 9x/2 remade into a sphere, and finally water in a lying cylinder of length 150 cm and radius 20 cm at depth 5 cm.

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

Part (ai) · 1 mark

Find the cuboid's volume from its three edge lengths.

  1. 1Volume = 20 × 12 × 5 = 1200 cm³

Answer1200

Part (aiia) · 3 marks

Work out the total area of all six faces of the cuboid.

  1. 1Faces: 20 × 12 = 240, 20 × 5 = 100, 12 × 5 = 60
  2. 2Total = 2 × (240 + 100 + 60)
  3. 3= 2 × 400 = 800 cm²

Answer800

Part (aiib) · 1 mark

Using $1.52 as the painting cost, determine the price in cents for one square centimetre.

  1. 1$1.52 = 152 cents
  2. 2152 ÷ 800 = 0.19 cents

Answer0.19

Part (b) · 3 marks

After melting the cylinder, express the sphere's radius r using x, given V = 4/3πr³.

  1. 1Cylinder volume = πx² × 9x/2 = 9πx³/2
  2. 24/3 πr³ = 9πx³/2
  3. 3r³ = 27x³/8
  4. 4r = 3x/2

Answer(3x)/2 or 1.5x

Part (c) · 7 marks

For the horizontal cylinder with radius 20 cm and water depth 5 cm, find the water volume in litres.

  1. 1Centre O, chord AB is the water surface: cos(½ AOB) = (20 − 5)/20 = 0.75
  2. 2Angle AOB = 2 × cos⁻¹(0.75) = 82.82°
  3. 3Sector = 82.82/360 × π × 20² = 289.09… cm²
  4. 4Triangle AOB = 1/2 × 20² × sin 82.82° = 198.43… cm²
  5. 5Segment = 289.09 − 198.43 = 90.66… cm²; volume = 90.66 × 150 = 13 599 cm³
  6. 613 599 ÷ 1000 = 13.599… ≈ 13.6 litres

Answer13.6 or 13.59 to 13.61

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Also searched as: 0580/43/M/J/21 · 0580_s21_qp_43 · 0580 s21 43 · question 8.
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