Unit 3: Geometry and Trigonometry
Topic 3.1: Three-Dimensional Geometry Questions
Practice 20 exam-style questions for IB Math AA SL Topic 3.1. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Find2 marks
2026• Aimnova practice — 3.1.1
Find the midpoint of A(2, −1, 4) and B(6, 3, 10).
Markscheme and model answer locked
Unlock Question2Find2 marks
2026• Aimnova practice — 3.1.1
Find the distance between A(1, −2, 3) and B(4, 2, 3).
Markscheme and model answer locked
Unlock Question3Find2 marks
2026• Aimnova practice — 3.1.1
Find the distance between A(2, 3, 6) and B(2, 3, 6)... no — find the distance between P(0, 0, 0) and Q(2, 3, 6).
Markscheme and model answer locked
Unlock Question4Find2 marks
2026• Aimnova practice — 3.1.2
Find the volume of a cylinder with base radius 5 and height 12.
Markscheme and model answer locked
Unlock Question5Find2 marks
2026• Aimnova practice — 3.1.3
Find the length of a face diagonal of a cube of side 5.
Markscheme and model answer locked
Unlock Question6State2 marks
2026• Aimnova practice — 3.1.3
A point P lies on a circle with diameter [AB]. State the size of angle APB and give the reason.
Markscheme and model answer locked
Unlock Question7Find2 marks
2026• Aimnova practice — 3.1.3
A right-angled triangle inside a solid has the angle θ with opposite side 7 and hypotenuse 25. Find θ.
Markscheme and model answer locked
Unlock Question8Find2 marks
2026• Aimnova practice — 3.1.2
Find the volume of a square-based pyramid with base side 6 and vertical height 10.
Markscheme and model answer locked
Unlock Question9Find2 marks
2026• Aimnova practice — 3.1.2
A cylinder has volume 200π cm³ and height 8 cm. Find its base radius.
Markscheme and model answer locked
Unlock Question10Find3 marks
2026• Aimnova practice — 3.1.2
A cone has base radius 6 and slant height 10. Find its total surface area.
Markscheme and model answer locked
Unlock Question11Find3 marks
2026• Aimnova practice — 3.1.1
M(3, 2, 5) is the midpoint of A(1, 0, 2) and B. Find the coordinates of B.
Markscheme and model answer locked
Unlock Question12Find2 marks
2026• Aimnova practice — 3.1.1
A cuboid has one vertex at the origin and the opposite vertex at (3, 4, 12). Find the length of its space diagonal.
Markscheme and model answer locked
Unlock Question13Find3 marks
2026• Aimnova practice — 3.1.2
A cone has base radius 6 and vertical height 8. Find its slant height, then its curved surface area.
Markscheme and model answer locked
Unlock Question14Find3 marks
2026• Aimnova practice — 3.1.2
A sphere has volume 288π. Find its radius.
Markscheme and model answer locked
Unlock Question15Find3 marks
2026• Aimnova practice — 3.1.3
A vertical mast of height 8 m stands on horizontal ground. A cable runs from its top to a point on the ground 15 m from its base. Find the angle the cable makes with the ground.
Markscheme and model answer locked
Unlock Question16Find3 marks
2026• Aimnova practice — 3.1.1
Find (a) the distance and (b) the midpoint of A(0, 1, 2) and B(4, 1, 8).
Markscheme and model answer locked
Unlock Question17Find3 marks
2026• Aimnova practice — 3.1.3
From the top of a 40 m cliff, the angle of depression to a boat is needed... no — a flagpole of height 6 m sits on a 10 m tower. Find the angle of elevation from a point 20 m from the base to the TOP of the flagpole.
Markscheme and model answer locked
Unlock Question18Find3 marks
2026• Aimnova practice — 3.1.2
A solid consists of a cylinder (radius 3, height 10) with a hemisphere (radius 3) on top. Find its total volume.
Markscheme and model answer locked
Unlock Question19Find4 marks
2026• Aimnova practice — 3.1.3
A square-based pyramid has base side 8 and the apex directly above the centre at height 3. Find the angle between a slant edge and the base.
Markscheme and model answer locked
Unlock Question20Find4 marks
2026• Aimnova practice — 3.1.3
A cuboid has a base 6 by 8 and height 5. A diagonal runs from a bottom corner to the opposite top corner. (a) Find the base diagonal. (b) Find the angle the space diagonal makes with the base.
Markscheme and model answer locked
Unlock QuestionReady to practice Topic 3.1?
Get instant AI feedback on your answers, view detailed markschemes, and track your progress across all IB Math AA SL topics.