Areas must be multiplied by the square of the conversion factor, and volumes by its cube.

e.g. 1cm = 10mm, 1cm(squared) = 100mm(squared), 1cm(cubed) = 1000mm(cubed)

When analysing a mathematical formula, regard numbers as dimensionless.

e.g. (pi) x r(squared) = (dimensionless) x (length) x (length)

This is length(squared) which is an area.

For 1/3 x (pi) x r(squared) x h, both 1/3 and pi are dimensionless. Therefore, the formula has dimensions: length(squared) x length = length(cubed) which is a volume

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