You can find volume by counting unit cubes in layers. For a rectangular prism (a box shape), the counting turns into a formula.
Key idea
$V = l \times w \times h$: length times width gives the cubes in one layer, and times the height counts the layers. Volume is measured in cubic units, such as cubic centimeters ($\text{cm}^{3}$).
Why it works
A box 5 cm long and 3 cm wide holds 5 rows of 3 one-centimeter cubes in its bottom layer: $5 \times 3 = 15$. If it is 4 cm high, there are 4 layers: $15 \times 4 = 60$ cubes. Each cube is 1 cubic centimeter, so the volume is 60 cubic centimeters.
Worked examples
Worked example: A box
Find the volume of a box 5 cm long, 3 cm wide and 4 cm high.
- $V = 5 \times 3 \times 4$.
- $5 \times 3 = 15$, and $15 \times 4 = 60$.
Answer: 60 cubic centimeters
Worked example: A cube
A cube has edges 6 inches long. What is its volume?
- All three edges are 6.
- $6 \times 6 \times 6 = 36 \times 6 = 216$.
Answer: 216 cubic inches
Common mistake
Adding the three edges ($5 + 3 + 4 = 12$) or writing square units. Adding edges does not count cubes, and square units measure flat area. Check: picture the cubes in one layer, then count the layers.