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.
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2026
Write down the coordinates of .
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A tin of soup is a cylinder with base radius 4 cm and height 9 cm. Calculate its volume, in terms of π.
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2026
A point P lies on a circle with diameter [AB]. State the size of angle APB and give the reason.
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2025
Show that the point is units from the origin.
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A point P lies on a circle and [AB] is a diameter of that circle. State the size of angle APB.
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2026
A right-angled triangle inside a solid has the angle θ with opposite side 7 and hypotenuse 25. Find θ.
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2026
Find the distance between P(0, 0, 0) and Q(2, 3, 6).
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A(−3, 2, 1) and C(7, 6, 9) are opposite corners of the square base of a pyramid. Find the coordinates of the centre of the base.
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2026
Find the distance between and ... no — find the distance between and .
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2026
Find the volume of a square-based pyramid with base side 6 and vertical height 10.
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2024
A closed cylinder has height equal to its diameter. Show that its total surface area is , where is its radius.
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2026
The points A(−2, 3, 1) and B(4, −1, 5) lie on the surface of a sphere with centre C(1, 1, 3), and [AB] is a diameter.
Show that the radius of the sphere is √17.
Show that the radius of the sphere is √17.
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A square-based pyramid has base side 9 cm and vertical height 10 cm. Find its volume.
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Inside a solid, a right-angled triangle has the side opposite angle θ equal to 9 cm and the hypotenuse equal to 41 cm. Find θ, to 3 s.f.
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2026
Find the distance between A(1, −2, 3) and B(4, 2, 3).
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2026
A cone has base radius r cm and height h cm, and a volume of 300 cm3.
Show that h = 900/(πr2).
Show that h = 900/(πr2).
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2026
Find the volume of a cylinder with base radius 5 and height 12.
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2026
Find the midpoint of A(2, −1, 4) and B(6, 3, 10).
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2024
Write down the coordinates of the midpoint of and .
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