Volume Vocabulary
Build the Layers
Find the Volume
Expressions & Equations
Volume Detectives
100
What is a unit cube
A cube that measures 1 unit × 1 unit × 1 unit and has a volume of 1 cubic unit.
100
A rectangular prism has a base that is 4 cubes long and 3 cubes wide.
How many cubes are needed to build ONE complete layer?
Answer: 12 cubes
4 × 3 = 12
100
Basic Dimensions
A rectangular prism is 4 units long, 2 units wide, and 3 units high.
What is the volume?
4 × 2 × 3 = 24 cubic units
100
A rectangular prism is 5 units long, 2 units wide, and 3 units high.
Which expression represents its volume?
A. 5 + 2 + 3
B. 5 × 2 × 3
C. 5 × 2 + 3
D. 5 + 2 × 3
B. 5 × 2 × 3
100
Find the Mistake
A student finds the volume of a prism with dimensions 5 × 2 × 3 like this:
5 + 2 + 3 = 10 cubic units
What mistake did the student make?
The student added the dimensions instead of multiplying them.
Correct: 5 × 2 × 3 = 30 cubic units
200
Why do we measure volume in cubic units instead of square units?
Answer:
Because volume measures the space inside a 3-dimensional figure using unit cubes.
Examples: cm³, in³, ft³
200
A rectangular prism has 15 cubes in each complete layer.
If the prism has 3 equal layers, how many cubes fill the entire prism?
Answer: 45 cubic units
15 × 3 = 45
200
A rectangular prism has a base area of 15 square units and a height of 4 units.
What is the volume?
15 × 4 = 60 cubic units
200
What Do the Factors Mean?
A prism has 8 cubes in each layer and 4 layers.
The expression 8 × 4 represents its volume.
What does each factor represent?
8 = cubes in each complete layer
4 = number of layers
200
Missing Height
A rectangular prism has a base area of 12 square units and a volume of 48 cubic units.
What is the missing height?
Answer: 4 units
12 × 4 = 48
300
In a rectangular prism, what does the base help us determine when finding volume?
The base helps us determine how many unit cubes are in one complete layer.
Area of Base = length × width
300
A rectangular prism has a volume of 48 cubic units. Each complete layer contains 12 cubes.
How many equal layers does the prism have?
Answer: 4 layers
48 ÷ 12 = 4
300
A rectangular prism has 12 unit cubes in each complete layer. There are 5 equal layers.
What is the volume?
12 × 5 = 60 cubic units
300
Match the Prism
Three prisms have these dimensions:
Prism A: 3 × 3 × 4
Prism B: 6 × 2 × 3
Prism C: 4 × 2 × 5
Which prism can be represented by the expression:
(6 × 2) × 3
Prism B
Why?
6 × 2 represents the area of the base, and 3 represents the height/number of layers.
300
Who Is Correct?
A prism has 15 cubes in each layer and 4 layers.
- Maya: 15 + 4 = 19 cubic units
- Jordan: 15 × 4 = 60 cubic units
Who is correct, and why?
Answer: Jordan because volume can be found by multiplying the cubes in one complete layer by the number of equal layers.
15 × 4 = 60 cubic units
400
A rectangular prism has 6 equal layers of cubes.
What is the height, and what does the height tell us?
The height is 6 units. It tells us there are 6 equal layers stacked in the prism.
400
A rectangular prism is only partially filled with cubes. You can see that its base is 5 cubes long and 2 cubes wide, and the prism is 4 cubes high.
How can you determine the volume without filling in or counting every cube?
Answer:
Find one complete layer:
5 × 2 = 10 cubes per layer
Then multiply by the number of layers:
10 × 4 = 40 cubic units
⭐ Volume = 40 cubic units
400
A storage box is shaped like a rectangular prism. It measures:
8 inches long × 3 inches wide × 4 inches high
What is the volume of the box?
8 × 3 × 4 = 96 cubic inches
400
Which Expression Belongs?
A rectangular prism has a base that is 7 units long and 3 units wide. It is 4 units high.
Which TWO expressions can be used to find its volume?
A. 7 × 3 × 4
B. 21 × 4
C. 7 + 3 + 4
D. 10 × 4
A and B
Because:
7 × 3 = 21 cubes in one layer
So:
7 × 3 × 4 = 21 × 4 = 84 cubic units
400
Missing Dimension Detective
A rectangular prism has a volume of 72 cubic units.
- Length = 6 units
- Width = 3 units
- Height = ?
What is the missing height?
Answer: 4 units
6 × 3 = 18
72 ÷ 18 = 4
500
I am a 3-D solid figure with 6 rectangular faces. You can find the amount of space inside me by multiplying my length × width × height.
What am I, and what is the measurement of the space inside me called?
The figure is a right rectangular prism, and the amount of space inside it is called volume.
500
A rectangular prism will have a volume of 96 cubic units when completely filled.
One complete layer contains 16 unit cubes.
The prism currently has 2 complete layers built.
How many MORE complete layers are needed to finish the prism?
Answer:
96 ÷ 16 = 6 total layers
6 − 2 = 4 more layers
✅ 4 additional complete layers are needed.
500
A rectangular prism has a volume of 120 cubic units. Its base is 5 units long and 4 units wide.
What is the height of the prism?
Answer:
5 × 4 = 20 square units in the base
120 ÷ 20 = 6 units high
500
Expression Detective
Jada says the expression 12 × 5 represents the volume of a rectangular prism.
Marcus says:
“The 12 must be the length of the prism, and the 5 must be the width.”
Is Marcus correct? Explain what 12 and 5 could represent.
No.
12 could represent the number of cubes in one complete layer (area of the base), and 5 could represent the number of equal layers (height).
Therefore:
12 × 5 = 60 cubic units.
500
Challenge: Same Volume, Different Prism
Prism A has dimensions:
5 × 2 × 6
Prism B has:
- Length = 3 units
- Width = 4 units
- Height = ?
Both prisms have the same volume.
What is the missing height of Prism B? Explain how you know.
Prism A:
5 × 2 × 6 = 60 cubic units
Prism B's base:
3 × 4 = 12 square units
60 ÷ 12 = 5 units
✅ Height = 5 units