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0580/42 Oct/Nov 2021, Question 7: Composite Perimeter, Area and Volume

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 13 marks

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The question, in short

Container of hemisphere, cylinder and cone each radius 2 m, cylinder height 5.2 m, cone height h m; find hemisphere volume, h from total volume 88π/3 m³, emptying time, and circle radius from segment area 65 cm².

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

Part (ai) · 2 marks

Calculate the volume of the hemisphere with radius 2 m, giving the answer as a multiple of π.

  1. 1Hemisphere = 1/2 × 4/3 × π × 2³
  2. 2= 16π/3 m³

Answer16π/3 or 5 1/3 π

Part (aii) · 4 marks

Given total volume 88π/3 m³, calculate h, the cone height, using radius 2 m and cylinder height 5.2 m.

  1. 1Hemisphere = 1/2 × 4/3 × π × 2³ = 16π/3
  2. 2Cylinder = π × 2² × 5.2 = 20.8π
  3. 3Cone = 1/3 × π × 2² × h = 4πh/3
  4. 416π/3 + 20.8π + 4πh/3 = 88π/3, so 4h/3 = 24 − 20.8 = 3.2
  5. 5h = 3.2 × 3 ÷ 4 = 2.40

Answer2.40

Part (aiii) · 3 marks

Container full of grain emptied at 35000 kg per hour, 1 m³ grain has mass 620 kg; find time in hours and minutes.

  1. 1Mass = 88π/3 × 620 = 57 135.09… kg
  2. 2Time = 57 135.09… ÷ 35 000 = 1.6324… hours
  3. 30.6324… × 60 = 37.9 minutes
  4. 4Time = 1 hour 38 min

Answer1 hour 38 min or 1 hour 37.8 min to 1 hour 37.9… min

Part (b) · 4 marks

Circle centre O radius r cm, angle AOB = 140°, shaded segment area 65 cm²; calculate r.

  1. 1Segment = sector − triangle
  2. 2140/360 × π × r² − 1/2 × r² × sin 140° = 65
  3. 3r² × 0.90033… = 65, so r² = 72.195…
  4. 4r = 8.496… ≈ 8.50 cm

Answer8.50 or 8.496 to 8.497

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Also searched as: 0580/42/O/N/21 · 0580_w21_qp_42 · 0580 w21 42 · question 7.
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