What is Solids and their vocabulary? — Mathematics

Definition 35.1 Primary & Middle School Mathematics · Chapter 35 — Cubes and Boxes

A solid occupies space. Flat sides are faces; faces meet along edges; edges meet at vertices. The family portraits:

the cube: $6$ square faces, $12$ edges, $8$ vertices;
the box (rectangular prism): $6$ rectangular faces, $12$ edges, $8$ vertices;
the cylinder: two disk faces and one rolled face (a can);
the pyramid: a polygon base and triangles meeting at an apex;
the ball (sphere): one perfectly round surface, no face, no edge.

The solid gallery. Dashed lines show hidden edges — the back of the solid, seen through it.

Examples

Example 35.2 (Counting on the cube)

Check on a die: $6$ faces (the numbers $1$ to $6$ ), $8$ vertices (the corners), $12$ edges (run a finger along them: $4$ on top, $4$ at the bottom, $4$ vertical). And $6 + 8 = 12 + 2$ — the same curious pattern holds for the box and the pyramid (Example 62.2 returns to it).

Example 35.4 (Reading a net)

On a die, opposite faces add up to $7$ . On a net, opposite faces are the ones separated by exactly one square in a row (or around a corner) — not the neighbors! Marking the pairs on the net before folding is a great exercise in seeing space flat.

Example 35.6 (Counting a box layer by layer)

A box $4$ cubes long, $3$ wide, $2$ high: the bottom layer holds $4 \times 3 = 12$ cubes, and there are $2$ layers:

12 \times 2 = 24 \text{ cubes} .

Counting by layers always works — and it quietly proves the formula $V = L \times w \times h$ of Chapter 43.

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Examples

Related terms