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
Comments
No comments have yet been made