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0580/42 May/Jun 2024, Question 4: Area of a Sector

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 15 marks

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The question, in short

Half-cylinder tank radius 12 cm, length 1 m, filled with water; find water volumes before and after draining, mass of a stone from a rectangular tank, and angle of cuboid diagonal AG with its base.

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

Part (ai) · 3 marks

Calculate the volume of water in the full half-cylinder tank, giving the answer to the nearest 10 cm³.

  1. 1Length = 1 m = 100 cm
  2. 2Volume = 1/2 × π × 12² × 100 = 7200π
  3. 3= 22 619.4… ≈ 22 620 cm³

Answer22620

Part (aii) · 5 marks

With the water level 6 cm below the top, calculate the volume of water remaining in the tank.

  1. 1The centre is on the top edge; the water surface is a chord 6 cm below it
  2. 2Half the angle at the centre: cos θ = 6/12, so θ = 60° and the full angle is 120°
  3. 3Sector = 120/360 × π × 12² = 150.79…; triangle = 1/2 × 12² × sin 120° = 62.35…
  4. 4Water cross-section = 150.79… − 62.35… = 88.44… cm²
  5. 5Volume = 88.44… × 100 = 8844 ≈ 8840 cm³

Answer8840 or 8850 or 8836 to 8850

Part (b) · 3 marks

Using the 0.2 cm depth drop in a 42 cm by 35 cm tank and stone density 2.2 g/cm³, calculate the stone's mass.

  1. 1Volume of stone = 42 × 35 × 0.2 = 294 cm³
  2. 2Mass = 2.2 × 294 = 646.8 g

Answer647 or 646.8

Part (c) · 4 marks

For cuboid ABCDEFGH with AB = 8 cm, BC = 12 cm and CG = 15 cm, calculate the angle AG makes with the base.

  1. 1AC² = 8² + 12² = 208, AC = 14.42…
  2. 2The angle is GAC: tan GAC = 15/14.42…
  3. 3Angle = 46.12…° ≈ 46.1°

Answer46.1 or 46.12 to 46.14

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Also searched as: 0580/42/M/J/24 · 0580_s24_qp_42 · 0580 s24 42 · question 4.
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