Surface Area and Volume | Their Difference

Geometry involves many interesting analysis. One of the key items is the computation of Surface Area. Another is the Volume of various 3-dimensional shapes.

What is the main difference between these 2 parameters of geometrical study?

Surface Area: The study of total areas on the outer surface. It is what user can feel.

Volume: The study of how much the shape (or object) can contain within its boundaries.

Let me explain more using a simple cube.


Let me start with surface area of the cube (diagram above).

It has 6 equal surfaces (being a cube for this example only)

If the length of one edge is, say, A units, then the surface area of ONE side is A² unit².

Total surface area = 6 x (A²) unit² = 6A² unit².
This is the total area of all surfaces that any person can feel (physically). OK? Clear?

If Surface Area is understood, then let's move on to Volume.

Volume is the amount of stuffs we can fill the object in question with (totally without gaps).

Volume for the cube (above) = width x length x height

(This formula is specific to cubic structure).

Interpretation of Volume, from the formula, is actually,
Area x Height!

Answer of Volume for the cube = A x A x A unit³ = A ³ unit³ .

Note: For the same object, the numerical value for surface area may not be smaller than its volume.

Common mistakes made:
- Missing out on some surfaces (or inability to visualise ==> need more practices)
- Wrong unit dimensioning (Area: unit² and Volume: unit³)

:P