Unit 3: Geometry and Trigonometry
Topic 3.1: Volumes and Surface Areas of 3D Shapes Questions
Practice 20 exam-style questions for IB Math AI SL Topic 3.1. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Find3 marks
2022• AI SL P1
Two cafes are at A(1, 3) and B(7, 7) on a coordinate grid where 1 unit = 1 km. Find the exact distance AB.
Markscheme and model answer locked
Unlock Question2find2 marks
A cone fits perfectly inside a cylinder (same r, same h). Show that Vcone = ⅓ Vcylinder.
Markscheme and model answer locked
Unlock Question3Calculate1 mark
2023• AI SL P1
Point P has coordinates (2, 5) and point Q has coordinates (8, 13). What is the distance PQ?
Markscheme and model answer locked
Unlock Question4find2 marks
Find the midpoint of A(1, 9) and B(7, 3).
Markscheme and model answer locked
Unlock Question5find2 marks
A circle has centre C(3, 5) and passes through point P(8, 17). Find the radius.
Markscheme and model answer locked
Unlock Question6find2 marks
A square-based prism has volume 200 cm³ and height 8 cm. Find the side of the base.
Markscheme and model answer locked
Unlock Question7find2 marks
Find the distance between A(2.5, 3.5) and B(8.5, 11.5).
Markscheme and model answer locked
Unlock Question8find2 marks
A cuboid has length 10 cm, width 6 cm, and height x cm. Its volume is 240 cm³. Find x.
Markscheme and model answer locked
Unlock Question9Find1 mark
2023• AI SL P1
Point A has coordinates (−3, 4) and point B has coordinates (5, −2). What are the coordinates of the midpoint M of [AB]?
Markscheme and model answer locked
Unlock Question10State1 mark
2022• AI SL P1
Two towns are at (0, 0) and (5, 12) on a coordinate grid where 1 unit = 1 km. What is the distance between the towns?
Markscheme and model answer locked
Unlock Question11find2 marks
Find the distance from the origin to the point (-9, 12).
Markscheme and model answer locked
Unlock Question12find3 marks
Find the distance from the origin to (3, 4) and to (5, 12). Which point is farther?
Markscheme and model answer locked
Unlock Question13find3 marks
Find the distance between A(2, 3) and B(7, 15).
Markscheme and model answer locked
Unlock Question14Find4 marks
2023• AI SL P1 TZ1
Point P has coordinates (−3, 2) and point Q has coordinates (15, −8). Point M is the midpoint of [PQ].
Markscheme and model answer locked
Unlock Question15find2 marks
Find the distance between A(0, 0) and B(6, 8).
Markscheme and model answer locked
Unlock Question16find2 marks
Find the midpoint of A(-5, 8) and B(11, -4).
Markscheme and model answer locked
Unlock Question17find2 marks
A surveyor places a point M at the midpoint of A(3, 12) and B(15, -4). Find the coordinates of M.
Markscheme and model answer locked
Unlock Question18find2 marks
A wedge is a triangular prism with base triangle vertices at (0,0), (4,0), (0,3). The prism length is 7. Find its volume.
Markscheme and model answer locked
Unlock Question19find3 marks
Two villages A(2, 5) and B(11, 17) are on a map where each unit represents 1 km. Find the straight-line distance between them.
Markscheme and model answer locked
Unlock Question20find2 marks
A pyramid has rectangular base 5 × 7 cm and vertical height 12 cm. Find its volume.
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 AI SL topics.