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
- Volume of a cube
- Surface area of a cube
- Volume of a rectangular block
- Surface area of a block
- From the volume to the height
- Volume of a cylinder in terms of π
- Volume of a cylinder with π = 3.14
- Lateral area of a cylinder
- Surface area of a cylinder
- From the volume to the height of a cylinder
- Practice: prisms and cylinders
- Volume of a pyramid
- Slant height of a lateral face
- Surface area of a pyramid
- Volume of a cone
- Slant height of a cone
- Lateral area of a cone
- Volume of a sphere
- Surface of a sphere
- From the surface to the radius
- Frustum of a pyramid
- Frustum of a cone
- Practice: pyramids, cones and spheres
- From cubic centimetres to litres
- From litres to cubic centimetres
- A water tank in litres
- A juice can in millilitres
- Boxes inside the package
- Comparing two volumes
- Solids review
- Solid geometry test
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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