Counting every cube is slow. Multiplying the three sides gives the same answer.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Why it works
One layer holds length × width cubes, and there are height layers of them.
Another way to say it
Volume is base area × height. The base area is that first layer.
Finding a missing side
If the volume is 60 and the base is 3 by 4, the height is 60 ÷ 12.
Where the formula comes from
Volume = length × width × height, because length × width gives the number of cubes in one layer and height counts the layers. The formula is a shortcut for the layered counting you already did — not a rule handed down.
The same formula, said differently
Volume = area of the base × height. This is the more general statement, and it will still be true for prisms whose base is a triangle or any other shape. Learning it in this form now means less to relearn later.
Running the formula backwards
Given a volume of 24 cubic units and a base area of 12, the height is 24 ÷ 12 = 2. Any one of the three measurements can be found from the other two, which makes the formula a tool rather than a one-way recipe.
Solids made of two boxes
A solid shaped like two boxes joined can be split into parts, each measured separately and then added. Or measure a larger box and subtract the missing piece. This is the composite-area strategy from Grade 3, one dimension up.
Step 2: Try It Yourself
Tap and try it out.
- Cubes in one layer4 × 3 = 12
- Layers3
- 4 × 3 × 336 cubic units
Counting every cube gives 36, and so does 4 × 3 × 3. The formula is a shortcut for the count.
Step 3: Watch an Example
One step at a time.
Watch Leo Find a Missing Height
A box has a volume of 60 cubic cm and a base 3 cm by 4 cm.
- Step 1
He works out the base area: 3 × 4 = 12.
Step 4: Your Turn
Practice makes it stick.
The Crate
Problem 1 of 3
A crate 5 by 4 by 3. What is its volume?
cubic units
The Missing Height
Problem 2 of 3
Volume 72, base 4 by 3. What is the height?
The Two Boxes
Problem 3 of 3
Two boxes side by side, one 24 cubic units and one 18. What is the total volume?
cubic units
Use the Formula
1 of 4
Volume of a 6 by 3 by 2 box?
2 of 4
Volume of a 5 by 5 by 4 box?
3 of 4
Volume 48, base 4 by 2. What is the height?
4 of 4
A base area of 15 and a height of 4. What is the volume?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Volume of a 7 by 3 by 2 box?
Question 2 of 2
What does base area × height give?
What You Learned
- Volume is length × width × height.
- It is also base area × height.
- Volumes of separate solids add together.