Solid geometry

Volume and surface of prisms, cylinders, pyramids, cones, spheres and frusta, and capacity in litres

The Solid geometry unit belongs to the Geometry and trigonometry section of Math Mental and has 31 lessons: volume and surface of prisms, cylinders, pyramids, cones, spheres and frusta, and capacity in litres.

Lessons in this unit

  1. Volume of a cube Lesson, 8 questions
  2. Surface area of a cube Lesson, 8 questions
  3. Volume of a rectangular block Lesson, 8 questions
  4. Surface area of a block Lesson, 8 questions
  5. From the volume to the height Lesson, 8 questions
  6. Volume of a cylinder in terms of π Lesson, 8 questions
  7. Volume of a cylinder with π = 3.14 Lesson, 8 questions
  8. Lateral area of a cylinder Lesson, 8 questions
  9. Surface area of a cylinder Lesson, 8 questions
  10. From the volume to the height of a cylinder Lesson, 8 questions
  11. Practice: prisms and cylinders Practice, 12 questions
  12. Volume of a pyramid Lesson, 8 questions
  13. Slant height of a lateral face Lesson, 8 questions
  14. Surface area of a pyramid Lesson, 8 questions
  15. Volume of a cone Lesson, 8 questions
  16. Slant height of a cone Lesson, 8 questions
  17. Lateral area of a cone Lesson, 8 questions
  18. Volume of a sphere Lesson, 8 questions
  19. Surface of a sphere Lesson, 8 questions
  20. From the surface to the radius Lesson, 8 questions
  21. Frustum of a pyramid Lesson, 8 questions
  22. Frustum of a cone Lesson, 8 questions
  23. Practice: pyramids, cones and spheres Practice, 12 questions
  24. From cubic centimetres to litres Lesson, 8 questions
  25. From litres to cubic centimetres Lesson, 8 questions
  26. A water tank in litres Lesson, 8 questions
  27. A juice can in millilitres Lesson, 8 questions
  28. Boxes inside the package Lesson, 8 questions
  29. Comparing two volumes Lesson, 8 questions
  30. Solids review Practice, 12 questions
  31. Solid geometry test Unit test, 15 questions

How to work through this unit

Follow the lesson order

The unit has 31 lessons of increasing difficulty. Finish one before moving on: the early techniques come back in the later questions.

Solve it before reading the solution

Work every question out on your own, then read the step by step and check the reason for each step instead of only comparing the final answer.

Lock it in during review

The question types you miss come back in practice and review until you get them right in a row. The unit test confirms the whole unit stuck.

Frequently asked questions about this unit

What does the Solid geometry unit cover?

Solid geometry belongs to the Geometry and trigonometry section and has 31 lessons: volume and surface of prisms, cylinders, pyramids, cones, spheres and frusta, and capacity in litres. The lessons start with the basic cases and build up to applications, always with a step-by-step solution.

What should I know before studying Solid geometry?

This page names the previous unit on the path. If it is not solid yet, go back and practice first; if there is no prerequisite, this is where the path begins.

How long does Solid geometry take?

Each lesson takes a few minutes. Most students do one or two a day and finish a unit in one or two weeks. The goal is answering correctly day after day, not clearing everything at once.

Are the Solid geometry exercises free?

Yes. Every Math Mental lesson is free and ad-free; you only need an account to save your progress.

Your first lesson takes five minutes

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