Surface Area and Volume

Study Sheet

Surface Area and Volume

Wrapping versus filling

Two Different Measures

Concept
The Big Idea
432

Volume fills the inside (cubic units). Surface area wraps the outside (square units) — add up the six faces, which come in matching pairs.

Example
A 4 by 3 by 2 box

Volume =4⋅3⋅2=24= 4 \cdot 3 \cdot 2 = 24. Surface area =2(12+6+8)=52= 2(12 + 6 + 8) = 52.

In Plain Terms & More Examples

Concept
In plain terms

Volume fills the inside (cubic units); surface area covers the outside (square units) — add the areas of all six faces.

Example
A cube of side 3

Volume =33=27= 3^3 = 27. Surface area =6×32=54= 6 \times 3^2 = 54.

Example
A 5 by 2 by 2 box

Volume =5⋅2⋅2=20= 5 \cdot 2 \cdot 2 = 20. Surface area =2(10+4+10)=48= 2(10 + 4 + 10) = 48.