In this chapter you meet volume for the first time. Volume tells you how much space a solid takes up inside – how much water fits into it, or how many unit cubes you would need to build it.
We start gently: count unit cubes first, then arrive at the formula V = a · b · c. You also learn to recognise a valid cube net and to compute the surface area of a cuboid from its net.
What you will learn
After the articles and exercises you should be able to:
understand what volume is and the units in which it is measured
compute the volume of a cuboid by counting unit cubes
use the formula V = a · b · c
recognise a valid cube net
compute the surface area of a cuboid from its net
Volume by counting unit cubes
A unit cube has all edges of length 1. If we use 1 cm edges, each unit cube has volume 1 cm³.
If a cuboid is built from unit cubes, its volume equals the number of unit cubes.
Example: a cuboid 4 cm long, 2 cm wide, 3 cm high contains 4 · 2 · 3 = 24 unit cubes. Its volume is 24 cm³.
Formula V = a · b · c
Multiply length, width, and height. The result is the volume in cubic units.
For a cube, all three are the same: V = a · a · a.
Cube net
A net is the unfolded version of a solid. The most familiar cube net is the cross: four squares in a row with one above and one below.
There are 11 distinct cube nets in total. Not every layout of 6 squares folds into a cube – a 2 × 3 rectangle, for example, does not.
Surface area from a net
The surface area of a cuboid is the sum of the areas of all 6 faces. Faces come in pairs:
