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0580/41 May/Jun 2025, Question 20: Frustum of a Cone

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 9 marks

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The question, in short

For a square-based pyramid with base side 10.5 cm and vertical height 24 cm, find the angle OA makes with the base, then the volume of a frustum of height 16 cm.

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Part (a) · 4 marks

Calculate the angle between edge OA and the square base, using base side 10.5 cm and pyramid height 24 cm.

  1. 1AC = √(10.5² + 10.5²) = 14.849…
  2. 2AM = 1/2 × 14.849… = 7.424…
  3. 3tan OAM = 24 ÷ 7.424…
  4. 4Angle OAM = 72.81… ≈ 72.8°

Answer72.8 or 72.81…

Part (b) · 5 marks

Calculate the volume of the frustum cut from the pyramid parallel to the base, with frustum height 16 cm.

  1. 1Small pyramid height = 24 − 16 = 8, so scale factor = 8/24 = 1/3
  2. 2Small base side = 10.5 × 1/3 = 3.5 cm
  3. 3Large pyramid = 1/3 × 10.5² × 24 = 882
  4. 4Small pyramid = 1/3 × 3.5² × 8 = 32.66…
  5. 5Frustum = 882 − 32.66… = 849.3… cm³

Answer849 1/3 or 849 or 849.3…

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Also searched as: 0580/41/M/J/25 · 0580_s25_qp_41 · 0580 s25 41 · question 20.
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