Lines and Order of Symmetry: Full Table of Plane Shapes
Math Education6 min read
Math Education
7 min read
Solid Shapes: Types, Properties, and Formulas
Published: 12.08.2026·Updated: 12.08.2026
Putri Anggraini
Head of Math Program, Algonova
A solid shape is a three-dimensional figure with length, width, and height, so it can be filled - meaning it has volume.
The difference from a plane shape: a plane shape answers how many tiles cover a floor, a solid answers how much water fits in a tank.
Seven Solids and Their Properties
| Solid | Faces | Edges | Vertices | Volume |
|---|---|---|---|---|
| Cube | 6 | 12 | 8 | side × side × side |
| Cuboid | 6 | 12 | 8 | l × w × h |
| Triangular prism | 5 | 9 | 6 | base area × height |
| Square pyramid | 5 | 8 | 5 | ⅓ × base area × height |
| Cylinder | 3 | 2 | 0 | π × r × r × h |
| Cone | 2 | 1 | 1 | ⅓ × π × r × r × h |
| Sphere | 1 | 0 | 0 | ⁴⁄₃ × π × r × r × r |
Surface areas have their own pages: cube, cuboid, cylinder, cone, and sphere.
The Volume Pattern That Halves the Memorising
Seven volume formulas look like a lot. In fact there are only two patterns:
- Prisms, cubes, cuboids, and cylinders are all base area times height. Only the base shape differs - square, rectangle, triangle, or circle.
- Pyramids and cones are all one third of that. A cone is simply a pyramid with a circular base.
The sphere stands alone and does need memorising.
A child who catches this remembers two sentences rather than seven formulas. And the reason for the one third can be shown physically: three cones of water poured into a cylinder of the same base and height fill it exactly.
Surface Area Is Not Volume
Volume answers how much fits inside. Surface area answers how much paper you need to wrap it.
The units differ: volume in cubic units such as cubic centimetres, surface area in square units. If the final answer carries cubic units, it is volume.
