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0580/41 May/Jun 2021, Question 3: Constructing Equations

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 8 marks

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The question, in short

Compare the total surface areas of a cone (radius 2.4 cm, slant height 6.3 cm) and a hemisphere to find the hemisphere's radius R, then find the volume left after removing the top of a cone (radius 7.6 cm, height 16 cm) leaving height 12 cm.

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Part (a) · 4 marks

Given the cone's radius 2.4 cm and slant height 6.3 cm, use the curved surface area formula to find R for the hemisphere whose total surface area matches the cone's.

  1. 1Cone total area = π × 2.4² + π × 2.4 × 6.3 = 20.88π
  2. 2Hemisphere total area = πR² + 1/2 × 4πR² = 3πR²
  3. 33πR² = 20.88π, so R² = 6.96
  4. 4R = √6.96 = 2.638… ≈ 2.64

Answer2.64 or 2.638…

Part (b) · 4 marks

A cone of radius 7.6 cm and height 16 cm is cut parallel to its base, leaving height 12 cm; work out the volume of what remains.

  1. 1Removed cone height = 16 − 12 = 4 cm, radius = 7.6 × 4/16 = 1.9 cm
  2. 2Large cone = 1/3 × π × 7.6² × 16 = 967.77…
  3. 3Small cone = 1/3 × π × 1.9² × 4 = 15.12…
  4. 4Volume = 967.77… − 15.12… = 952.65… ≈ 953 cm³

Answer953 or 952.6 to 952.8

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Also searched as: 0580/41/M/J/21 · 0580_s21_qp_41 · 0580 s21 41 · question 3.
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