EASA / CAR Part-66 · Module 1 · 1.3 Geometry · Cat A
Objective: a box has two different totals that people mix up, the space inside it and the skin around it. Change the three sides and watch volume and surface area move apart, then flatten the box into its net to see where the six faces come from.
Volume is cubic, surface area is square. Volume is in cm³ because three lengths are multiplied; surface area is in cm² because only two are. Checking the units of your answer is the quickest way to catch a wrong formula in the exam.
The six faces come in matching pairs, which is why the surface-area formula has a 2 outside the bracket: top and bottom are both l × w, front and back are both l × h, the two ends are both w × h. The net makes those three pairs obvious.
Doubling every side multiplies the volume by eight and the area by four. That is the square-cube law, and it is the reason large components are proportionally heavier than small ones, and why the area-to-volume ratio falls as things get bigger.