Volume of a Box
“Volume is the base area times the height — length × width × height.”
The formula
V = a × b × cHow to read it: Volume is length times width times height — the base area times how tall it is
- a
- — the length
- b
- — the width
- c
- — the height
The hook
How many 1 cm cubes fit inside a box? That count is exactly its volume.
In plain words
The amount of space a solid takes up, counted as how many 1 cm cubes fit inside.
The intuition
Cover the bottom with 1 cm cubes and you fit 'length × width' of them in one layer. Stack that layer 'height' times, so volume = length × width × height — the base area multiplied once more by height.
How it's built
First find the base area (length × width), then multiply by the height. Three edge lengths give the volume. The unit is cubic, like cm³.
Example
A box 2 by 3 by 4: 2 × 3 × 4 = 24.
Common mistake
Volume is not surface area. Volume is how much fills the inside; surface area is the outer skin. Remember volume uses cubic units (cm³).
Where it's used
How much a tank or box holds, package sizes, the air in a room.
Where it came from
Volume math grew from practical needs — measuring grain stores and water in many ancient cultures.
Prerequisites
Quick check
What is the volume of a cube with every edge 2?
- 4
- 6
- 8✓
- 12
Practice
Find the volume of a box 3 by 4 by 5.
Answer: 60
- Volume = length × width × height
- 3 × 4 = 12
- 12 × 5 = 60
Takeaway: Multiply all three edges.
Find the volume of a cube with every edge 3.
Answer: 27
- A cube has three equal edges.
- 3 × 3 × 3 = 27
Takeaway: Cube volume = edge × edge × edge.
Find the volume of a box 10 by 1 by 2.
Answer: 20
- 10 × 1 = 10
- 10 × 2 = 20
Takeaway: Even a long thin box is just the three edges multiplied.