Dimensions of length, area and volume
The following rules apply for length, area and volume:
Length: one dimensional, length, units are mm, cm, m, km, inch foot
Area: two dimensional, length x length, units are mm², cm², m², hectare, km², square inch, square foot
Volume: three dimensional, length x length x length, units are mm³, cm³, m³, cubic inch, cubic foot
Using dimensions to check formulas
Dimensions can be used to check if a formula is correct to find out if it represents a length, area or volume.
Note: L in brackets [L] represents a dimension of length.
When checking the length of a perimeter: the formula is length [L] + length [L] + length [L]
Note: multiple [L] added together will still be [L]
Area on the other hand area is two-dimensional, therefore it is derived from multiplying two lengths together.
For example: [L] × [L] = [L²]
If more than two areas are added together, it is still an area, therefore: [L²] + [L²] = [L²]
Volumes is three dimensional and is derived by multiplying three lengths together, therefore [L] × [L] × [L] = [L³]
Consistency in formulas
Inconsistent formulas includes an expression where 2 dimensions are added to an expression with 3 dimensions.
Therefore only the following can be added together:
- Lengths to lengths
- Areas to areas
- Volumes to volumes