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.
1find2 marks
A cubic block of metal of side 5 cm is melted and reshaped into a cube of side x cm. Find x. (Trivial — show why.)
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A cone fits perfectly inside a cylinder (same r, same h). Show that Vcone = ⅓ Vcylinder.
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A storage box is a cuboid 60 × 40 × 30 cm.
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A cone has radius 6 cm and vertical height 8 cm. Find its volume.
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A circle has centre C(3, 5) and passes through point P(8, 17). Find the radius.
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2023
Point P has coordinates (−3, 2) and point Q has coordinates (15, −8). Point M is the midpoint of [PQ].
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2023
A cone has radius r and slant height l. What is its curved surface area?
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2022
A closed cylinder has radius 4 cm and height 10 cm.
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A drone flies in a straight line from P(−3, 2, 7) to Q(3, −1, 1), where the units are metres. Find the distance it flies, and the coordinates of the point exactly halfway along its path.
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A square-based pyramid has base side 6 cm and vertical height 8 cm. Find its volume.
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A cylinder has radius 3 cm and height 10 cm. Find its TOTAL surface area (closed).
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Find the distance from the origin to the point (-9, 12).
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2023
Point A has coordinates (−3, 4) and point B has coordinates (5, −2). What are the coordinates of the midpoint M of [AB]?
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A square-based prism has volume 200 cm³ and height 8 cm. Find the side of the base.
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A pyramid has a rectangular base 5 × 4 cm and a vertical height of 9 cm. Find its volume.
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2022
A cylinder has radius 5 cm and height 8 cm. What is its curved surface area?
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A solid is a cube of side 10 cm. Find its volume and surface area.
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2023
To find the slant height of a cone with vertical height h and base radius r, which formula is used?
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The points A(1, −2, 4) and B(5, 4, −2) are the ends of a straight tunnel. Find the length AB, correct to three significant figures, and the coordinates of the midpoint of [AB].
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