Lemmara logoLemmaraWorked solution

0580/42 May/Jun 2026, Question 16: Trigonometry in 3D: Pyramids and Cones

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 9 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Square-based pyramid ABCDE with apex A, diagonals EC and BD meeting at F, AF perpendicular to base, AF = 28 cm, BC = 16.5 cm. Find symmetry planes, volume, AB, and angle between AB and base.

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

Part (a) · 1 mark

State how many planes of symmetry the square-based pyramid has.

  1. 1Square-based right pyramid: 2 planes through the diagonals + 2 through midpoints of opposite sides
  2. 24 planes

Answer4

Part (b) · 2 marks

Calculate the volume of the pyramid using base side 16.5 cm and height 28 cm.

  1. 1V = 1/3 × base area × height
  2. 2= 1/3 × 16.5² × 28
  3. 3= 1/3 × 272.25 × 28 = 2541 cm³

Answer2541

Part (c) · 4 marks

Calculate the length AB from apex to a base vertex.

  1. 1BD² = 16.5² + 16.5² = 544.5, BD = 23.33…
  2. 2BF = ½BD = 11.667…, so BF² = 136.125
  3. 3AB² = 28² + 136.125 = 920.125
  4. 4AB = 30.3 cm

Answer30.3 or 30.33…

Part (d) · 2 marks

Calculate the angle between edge AB and the base plane BCDE.

  1. 1Required angle is angle ABF
  2. 2tan(ABF) = 28 ÷ 11.667 = 2.4
  3. 3angle ABF = 67.4°

Answer67.28 to 67.53…

Stuck on a step? Read the free lesson: Trigonometry in 3D: Pyramids and Cones

Practise more trigonometry in 3d: pyramids and cones questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on trigonometry in 3d: pyramids and cones

Also searched as: 0580/42/M/J/26 · 0580_s26_qp_42 · 0580 s26 42 · question 16.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.