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 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 Question2Find2 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 Question3Find2 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 Question4Find2 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 Question5Find2 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 Question6Find2 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 Question7State2 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 Question8Find2 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 Question9Find3 marks
2026• Aimnova practice — 3.1.4
A square-based right pyramid has apex V(2, 2, 8) and base centre X(2, 2, 0). (a) Write down the height VX. (b) The base has side 6. Find the exact length of the base diagonal AC.
Markscheme and model answer locked
Unlock Question10Find3 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 Question11Find3 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 Question12Find3 marks
2026• Aimnova practice — 3.1.2
A sphere has volume 288π. Find its radius.
Markscheme and model answer locked
Unlock Question13Find3 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 Question14Find2 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 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 Question16Find2 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 Question17Show5 marks
2026• Aimnova practice — 3.1.4
A solid hemisphere has its flat face centred at O(0, 0, 0) with radius 5. The point P(3, 0, 4) lies on the rim of the flat face. (a) Show that P lies on the rim. (b) Find the volume of the hemisphere.
Markscheme and model answer locked
Unlock Question18Find5 marks
2026• Aimnova practice — 3.1.4
A solid hemisphere has centre A(2, −1, 4) and the point B(2, −1, 10) lies on its curved surface. (a) Find the radius AB. (b) Find the total surface area of the solid hemisphere.
Markscheme and model answer locked
Unlock Question19Find3 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 Question20Find3 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 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.