This prism is made of 1-inch cubes. Find the volume of the prism.

Question

What expression could you use to find how many 1-inch cubes are needed to fill each layer of the prism?

2 in
3 in
5 in
Cubes in
each layer Number
of layers Volume
(
×
) ? ?
Good work!
How many layers of 1-inch cubes fit in the rectangular prism?

2 in
3 in
5 in
Cubes in
each layer Number
of layers Volume
( 3 × 2 )
?
Great job!
Now, find the volume of the prism. How many total 1-inch cubes fit in the rectangular prism?

2 in
3 in
5 in
Cubes in
each layer Number
of layers Volume
( 3 × 2 ) 5
in3

Answer 1

To find the volume of the prism made of 1-inch cubes, we can start by determining the dimensions given:

• Height = 5 inches
• Length = 3 inches
• Width = 2 inches

Step 1: Find the number of cubes in each layer

The volume of the layer (which is one layer of the rectangular prism) can be calculated as: \[ \text{Cubes in each layer} = \text{Length} \times \text{Width} = 3 \text{ in} \times 2 \text{ in} = 6 \text{ cubes} \]

Step 2: Find the number of layers

To find the number of layers, we take the height of the prism: \[ \text{Number of layers} = \text{Height} = 5 \text{ in} \]

Step 3: Find the total volume of the prism

The total volume of the prism can be found by multiplying the number of cubes in each layer by the number of layers: \[ \text{Volume} = \text{Cubes in each layer} \times \text{Number of layers} = 6 \text{ cubes} \times 5 \text{ layers} = 30 \text{ cubic inches} \]

Final Answers:

• Cubes in each layer: 6 cubes
• Number of layers: 5 layers
• Total Volume: 30 cubic inches

Therefore, the volume of the prism is 30 in³ and it can hold 30 total 1-inch cubes.