Prism Layers Worksheet
Prism Layers Investigation
Volume as Repeated Layers • \(V = B \times h\)
Name:
Date: Class:
Mission
Architect Elena is packing modular supply crates for a new science lab. Each unit cube box measures 1 cm × 1 cm × 1 cm (\(1\text{ cm}^3\)). The storage crate base is 5 cm long and 3 cm wide, and the crate stands 4 cm tall.
1
Step 1: Lay the Foundation (Base Layer)
Layer 1 of 4
Length: 5 cm (5 cubes) Width: 3 cm
Single bottom layer (Height = 1 cm)
A. How many unit cubes cover the bottom of the crate in 1 layer?
Area of Base (\(B\)) = length × width =
cubes (\(\text{cm}^2\))
B. What is the volume of just this single layer?
\(\text{Volume of Layer 1} =\)
\(\text{cm}^3\)
2
Step 2: Stack the Layers (Repeat for Full Height)
Total Height: 4 Layers
Layer 4 Layer 3 Layer 2 Layer 1 (Base) Height = 4 cm (4 layers)
4 identical horizontal layers stacked
Complete the table as Elena adds each layer to the crate:
| Layer # | Cubes Added | Multiplication / Addition | Cumulative Volume |
|---|
| Layer 1 | 15 | \(15 \times 1\) | \(15\text{ cm}^3\) |
| Layer 2 | 15 | \(15 \times 2\) or \(15 + 15\) | |
| Layer 3 | | | |
| Layer 4 | | \(15 \times 4\) | |
3
Step 3: Connect the Formulas & Conclude
Synthesis
Base Area × Height:
\(V = B \times h\) (Base Layer × Number of Layers)
\(V =\)
×
=
\(\text{cm}^3\)
Length × Width × Height:
\(V = l \times w \times h\) (All 3 Dimensions)
\(V =\)
×
×
=
\(\text{cm}^3\)
Explain: In your own words, how does thinking about layers explain why multiplying base area by height gives the total volume of a prism?
Extension: If Elena adds 2 more identical layers to the crate, what is the new height and total volume?
New Vol =
\(\text{cm}^3\)
Standard: 5.MD.C.5.A • Modeling volume as repeated addition of unit cube layers Page 1 of 1
Prism Layers Practice Worksheet
Prism Layers Practice
Independent Problem Solving • \(V = B \times h = l \times w \times h\)
Name:
Date: Class:
Problem
Marcus is constructing a glass aquarium habitat for a marine biology lab. The tank is built using modular 1-foot cube sections (\(1\text{ ft}^3\)). The rectangular base of the tank measures 6 feet long and 2 feet wide, and the tank is 5 feet deep (tall).
1
Step 1: Calculate the Base Layer (\(B\))
Layer 1 (Bottom)
Length = 6 ft (6 cubes) Width = 2 ft
Bottom layer (Height = 1 ft)
A. How many cubic feet of space are in one single base layer?
Base Area (\(B\)) = length × width =
\(\text{ft}^2\) (cubes)
B. What is the volume of this first 1-foot layer?
\(\text{Volume of Layer 1} =\)
\(\text{ft}^3\)
2
Step 2: Track Cumulative Volume by Layer
Height: 5 Layers
Layer 5 Layer 4 Layer 3 Layer 2 Layer 1 (Base) Height = 5 ft (5 layers)
5 identical 1-ft layers stacked
Fill in each layer as Marcus builds up the tank:
| Layer | Cubes in Layer | Layer Calculation | Total Volume |
|---|
| Layer 1 | 12 | \(12 \times 1\) | \(12\text{ ft}^3\) |
| Layer 2 | 12 | \(12 \times 2\) or \(12 + 12\) | |
| Layer 3 | | \(12 \times 3\) | |
| Layer 4 | | | |
| Layer 5 | | \(12 \times 5\) | |
3
Step 3: Verify with Both Volume Formulas
Formula Check
Base Area × Height:
\(V = B \times h\) (Base Layer × Total Height)
\(V =\)
×
=
\(\text{ft}^3\)
Length × Width × Height:
\(V = l \times w \times h\) (All 3 Dimensions)
\(V =\)
×
×
=
\(\text{ft}^3\)
Apply Your Knowledge: If Marcus fills the aquarium with water up to only 3 layers high, how many cubic feet of water are in the tank? Explain using the concept of layers:
