Surface area and capacity
Surface area adds up the outside faces in squared units; volume and capacity measure the space inside in cubed units.
A worked example
A closed box 20 cm by 10 cm by 6 cm needs 2(20x10 + 20x6 + 10x6) = 760 cm² of material.
The mistake people actually make
A cone holds one third of the cylinder that shares its base and height. Keep imperial and metric separate. Cubic feet and cubic yards differ by 27, not by 3.