Prism Layers Practice Worksheet
Prism Layers Practice
Volume of Rectangular Prisms • Unit Cubes • Multi-Layer Models
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The Layer Rule for Volume
Find the number of unit cubes in one base layer, then multiply by the number of layers.
\(\text{Volume} = \text{Base Area} \times \text{Number of Layers}\)
Problem 1 • Guided Stacking 3 pts
3 Layers Length = 4 units Width = 3
Prism A: 4 units long, 3 units wide, 3 layers
Examine Prism A above. Each small cube has a volume of \(1\text{ unit}^3\).
a. Cubes in 1 base layer (\(4 \times 3\)): cubes
b. Number of identical layers stacked:
c. Total Volume (\(\text{Base Area} \times \text{Layers}\)): \(\text{units}^3\)
Problem 2 • 5-Layer Focus The Warehouse Block Stack
6 pts
A builder stacks cubic storage containers to create a large rectangular prism. The bottom layer has a length of 6 units and a width of 4 units. The builder stacks exactly 5 identical layers of containers.
5 Layers L5 L4 L3 L2 L1 Length = 6 units Width = 4 units
5 Vertical Layers • 6 × 4 Base
Part A: How many unit cubes are in one single layer (the base)? Show multiplication.
Part B: Since there are 5 identical layers, calculate the total volume of the entire prism.
Total Volume = \(\text{units}^3\)
Part C: Write two different number sentences that both equal this volume:
Method 1: \((l \times w) \times h\)
Method 2: \(\text{Base Area} \times \text{Layers}\)
Unit: 5.MD.C.3 • 5.MD.C.5 Volume Concepts Page 1 of 2 Turn over for multi-layer application problems →
Prism Layers Practice | Problem Solving & Layer Comparisons
Name: Page 2
Problem 3 • Layer Comparison 3 pts
Two architecture students build models using \(1\text{-cm}\) unit cubes:
Maya's Tower 5 Layers
- • Each layer: 4 cm long by 2 cm wide
- • Number of layers: 5 layers
Volume Calculation:
Leo's Tower 4 Layers
- • Each layer: 5 cm long by 2 cm wide
- • Number of layers: 4 layers
Volume Calculation:
Which tower has greater volume, or are they equal? Explain:
Problem 4 • Missing Dimension Mystery 4 pts
A toy chest is in the shape of a rectangular prism. The bottom layer has an area of \(21\text{ sq ft}\) (length = \(7\text{ ft}\), width = \(3\text{ ft}\)). The total volume of the chest is \(105\text{ cubic feet}\).
How many layers of 1-foot cubes fit inside this toy chest?
Formula: \(\text{Number of Layers} = \text{Total Volume} \div \text{Base Area}\)
Show Work Here:
Layers =
Problem 5 • Real-World Application The 5-Layer Celebration Cake
6 pts
Chef Mateo builds a 5-layer rectangular cake. Each layer is made of \(1\text{-inch}\) cake cubes. The base of every layer is \(8\text{ inches long}\) and \(5\text{ inches wide}\).
Part A (1 Layer)
Cubes in 1 single layer:
cubes/layer
Part B (All 5 Layers)
Total volume of 5 layers:
\(\text{in}^3\)
Part C (Tiered Slice)
Volume left if top 2 layers removed:
\(\text{in}^3\)
Mathematical Explanation (Explain your thinking)
Sam says: "A prism with 5 layers will always have a bigger volume than a prism with 3 layers."
Is Sam correct? Provide a counterexample or explanation to prove your answer:
Unit: 5.MD.C.3 • 5.MD.C.5 Volume Concepts Page 2 of 2 Completed Practice Set • Check your units!
