Dimensions of Formulae

Use dimensional reasoning to classify formulae and detect expressions that cannot represent a real measurement.

Curriculum rangeYears 9–11

2\pi r

2\pi r

dim 1

✓ Every term has dimension 1 -- this could be a formula for length.

Count how many length letters multiply together in each term (ignore numbers and π). 1 length = a length formula. 2 lengths multiplied = an area formula. 3 lengths multiplied = a volume formula. Every term in a valid formula must have the same dimension.