Volume is how much space a solid fills. Area covers a flat surface; volume fills a box.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The unit of measurement is a small cube.
Unit cube is a cube 1 unit long on every side. Its volume is 1 cubic unit.
Just count them
The volume of a solid built from unit cubes is simply how many cubes it took.
Why "cubic"
The answer is in cubic units because the thing being counted is a cube.
Volume is a count of unit cubes
Volume measures how much space a solid occupies, and we measure it by filling the solid with equal cubes and counting them. A unit cube is 1 by 1 by 1. This is exactly the area idea from Grade 3, moved into three dimensions.
Count in layers
A box 4 by 3 by 2 has a bottom layer of 4 × 3 = 12 cubes, and 2 such layers, giving 24. Counting layer by layer is far more reliable than counting cubes one at a time, and it leads directly to the formula.
Cubic units
Volume is measured in cubic centimetres, cubic metres and so on, written cm³ or m³. The little 3 records that three lengths were multiplied. Area used square units for two lengths; the pattern is consistent.
No gaps and no overlaps
As with area, the cubes must fill the space completely without overlapping, or the count means nothing. Cubes work for this because they stack perfectly — spheres would leave gaps, which is why nobody measures volume in marbles.
Step 2: Try It Yourself
The count and the formula are shown together, and always agree.
- Cubes in one layer4 × 3 = 12
- Layers2
- 4 × 3 × 224 cubic units
Counting every cube gives 24, and so does 4 × 3 × 2. The formula is a shortcut for the count.
Step 3: Watch an Example
One step at a time.
Watch Ana Count a Box
Ana counts the cubes in a box 4 by 3 by 2.
- Step 1
She counts one layer: 4 rows of 3, which is 12 cubes.
Step 4: Your Turn
Practice makes it stick.
The Small Box
Problem 1 of 2
A box 3 by 2 by 4 cubes. How many cubes in all?
cubes
The Layer
Problem 2 of 2
A box 5 by 4 cubes at the base. How many cubes in one layer?
cubes
Count the Cubes
1 of 4
A box 2 by 2 by 2. How many cubes?
2 of 4
A box 3 by 3 by 3. How many cubes?
3 of 4
A box 6 by 2 by 3. How many cubes?
4 of 4
What is the volume of one unit cube?
Step 5: Quick Check
Show what you know.
Question 1 of 2
A box 4 by 4 by 2. How many cubes?
Question 2 of 2
Why is volume measured in cubic units?
What You Learned
- Volume is how much space a solid fills.
- The unit is a cube 1 unit on every side.
- Counting the cubes gives the volume.