Geometry in 3D
3D geometry for IB Applications SL: coordinates, distance, midpoint, and the volumes and areas of prisms, pyramids, cones, cylinders and spheres.
3D geometry takes to space what you already know from the plane: every point has three coordinates, the distance and the midpoint are calculated with one extra component, and solids appear: prisms, pyramids, cylinders, cones and spheres. In this topic you calculate volumes and surface areas, use Pythagoras and trigonometry inside the solids to find lengths and angles, and solve context problems (water tanks, tents, balloons). In the exam almost everything is done with the calculator and a good diagram of the solid, so it is worth practising sketching before calculating.
Recommended order
Work through the sections in order: coordinates, distance and midpoint, then prisms and pyramids, and finally cylinders, cones and spheres. At the end you will find the IB exam questions grouped by type.
Trigonometry (topic 3) and plane geometry (topic 4).
Sections in this topic
Coordinates, distance and midpoint in 3D
Coordinates in space, distance between two points, midpoint and angles using trigonometry. IB Applications SL.
3 worked examples Section 2Prisms and pyramids: volume, area and angles
Volume and area of prisms and pyramids, slant height, and lengths and angles inside solids with Pythagoras and trigonometry. IB Applications SL.
3 worked examples Section 3Cylinders, cones and spheres
Volume and area of cylinders, cones and spheres, composite solids, radius changes and similarity with scale factor k. IB Applications SL.
3 worked examples End of topicIB exam questions for topic 5
IB exam questions on 3D geometry: coordinates, distance, and volume and area of prisms, pyramids, cylinders, cones and spheres, with step-by-step solutions.
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