What is Volume by counting? — Mathematics

Definition 35.5 Primary & Middle School Mathematics · Chapter 35 — Cubes and Boxes

The volume of a solid built from unit cubes is the number of cubes it contains. The unit can be the centimeter cube (cm $^3$ ) or the meter cube (m $^3$ ).

A 4 × 3 × 2 box of unit cubes, counted layer by layer. — A $4 \times 3 \times 2$ box of unit cubes, counted layer by layer.

Examples

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.

Example 35.7 (Same cubes, different shapes)

Eight unit cubes can build a $2 \times 2 \times 2$ cube, a $8 \times 1 \times 1$ stick, or a $4 \times 2 \times 1$ slab: three different solids, one volume ( $8$ cubes). Volume counts the material, not the shape.

Read in context →

Examples

Related terms