What is the length of the space diagonal of a cube with edge length 1 cm?
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Pythagoras and trigonometry in 3D Topical Past Papers.
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These Pythagoras and trigonometry in 3D Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Trigonometry (E6.6) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Apply Pythagoras' theorem and right-angled trigonometry to problems involving 3-D figures (e.g. cuboids, pyramids), finding lengths and angles between lines and faces.
What is the length of the space diagonal of a cube with edge length 1 cm?
A cube has edge length 4 cm. Find the length of its space diagonal (corner-to-opposite-corner) in surd form.
[1 mark]A cuboid has dimensions 6 cm by 4 cm by 12 cm. Find the length of its space diagonal, correct to 1 decimal place.
[2 marks]A cuboid has dimensions 5 cm by 5 cm by 12 cm. Find the angle, in degrees correct to 1 decimal place, between the space diagonal and the base of the cuboid.
[2 marks]For a cuboid with edges a, b and c, the space diagonal length d satisfies:
A square-based pyramid has base side 8 cm and perpendicular height (from base centre to apex) 6 cm.
Find the length of a slant edge (from a base corner to the apex), correct to 1 decimal place.
[2 marks]Find the angle between a slant edge and the base of the pyramid, correct to 1 decimal place.
[1 mark]A cuboid has dimensions 7 cm by 24 cm by 24 cm. Find the angle, correct to 1 decimal place, between the space diagonal and the LONGEST face.
[2 marks]A regular tetrahedron has edge length 6 cm. (All four faces are equilateral triangles.) Find the perpendicular height of the tetrahedron, correct to 1 decimal place. (Use the fact that the foot of the perpendicular from the apex falls on the centroid of the base, which is at distance 2 cm from each vertex of the base when the side is 6 cm.)
[2 marks]