Prism Power Worksheet
PRISM POWER
MASTERING THE VOLUME OF THREE-DIMENSIONAL SHAPES
Name:
Date:
Class:
Score:
Volume Blueprint Reference
Cube
\(V = s^3\)
Multiply side length by itself three times.
Rectangular Prism
\(V = l \cdot w \cdot h\)
Multiply length times width times height.
Triangular Prism
\(V = B \cdot H\)
\(B = \text{base area} = \frac{1}{2} b h\). Multiply base area by prism length.
LEVEL 1
Rectangular Builders
1 Find the total volume of the cube below:
4 cm 4 cm 4 cm
Show your step-by-step formula substitution.
Answer: ________________________
2 A shipping box has the following measurements. Calculate its internal volume:
6 m 5 m 3 m
Verify that units are squared or cubed correctly.
Answer: ________________________
3 Find the volume of this high-rise block model with the dimensions shown:
8.5 in 10 in 4 in
Carefully multiply the decimal value.
Answer: ________________________
Prism Power Math Labs Page 1 of 2
PRISM POWER: VOLUME EXPLORATIONS
Geometry Practice
LEVEL 2
Triangular Treks
4 Find the volume of the triangular prism. First calculate the area of the triangular base:
6 cm 4 cm 10 cm
\(B = \frac{1}{2} \cdot \text{base} \cdot \text{height}\). Volume = \(B \cdot H\).
Answer: ________________________
5 Determine the volume of this heavy metal triangular block:
8 in 5 in 12 in
Keep your work neat inside the grid above.
Answer: ________________________
LEVEL 3
Real-World Blueprints
6 The Aquascaping Challenge Rectangular Prism
An architect designs an exhibition aquarium shaped like a rectangular prism. The tank is 24 inches long, 12 inches wide, and 16 inches high. How many cubic inches of water are required to fill it to the brim?
Answer: _________________
7 The Wilderness Tent Triangular Prism
An A-frame camping tent is shaped like a triangular prism. The front entrance triangle has a base of 6 feet and a height of 5 feet. The tent length is 9 feet. Find the total volume of air enclosed inside the tent.
Answer: _________________
8 ARCHITECT'S CHALLENGE BONUS
A concrete model block is a rectangular prism with dimensions \(10\text{ cm} \times 5\text{ cm} \times 4\text{ cm}\). A cube-shaped hole with a side length of \(2\text{ cm}\) is drilled straight through the middle. What is the remaining volume of concrete?
Answer: _________________
Prism Power Math Labs Page 2 of 2
Prism Power Answer Key
PRISM POWER
TEACHER ANSWER KEY
MASTERING THE VOLUME OF THREE-DIMENSIONAL SHAPES
Name: Lenny (Teacher)
Date: 08/24/2026
Class: Geometry 101
Score: 100 / 100
Volume Blueprint Reference (Answers in Red)
Cube
\(V = s^3\)
Multiply side length by itself three times.
Rectangular Prism
\(V = l \cdot w \cdot h\)
Multiply length times width times height.
Triangular Prism
\(V = B \cdot H\)
\(B = \text{base area} = \frac{1}{2} b h\). Multiply base area by prism length.
LEVEL 1
Rectangular Builders
1 Find the total volume of the cube below:
4 cm 4 cm 4 cm
\(V = s^3\)
\(V = 4\text{ cm} \times 4\text{ cm} \times 4\text{ cm}\)
\(V = 16\text{ cm}^2 \times 4\text{ cm} = \mathbf{64\text{ cm}^3}\)
Formula substitute: \(4 \times 4 \times 4\)
Answer: \(64\text{ cm}^3\)
2 A shipping box has the following measurements. Calculate its internal volume:
6 m 5 m 3 m
\(V = l \cdot w \cdot h\)
\(V = 6\text{ m} \times 3\text{ m} \times 5\text{ m}\)
\(V = 18\text{ m}^2 \times 5\text{ m} = \mathbf{90\text{ m}^3}\)
Formula substitute: \(6 \times 3 \times 5\)
Answer: \(90\text{ m}^3\)
3 Find the volume of this high-rise block model with the dimensions shown:
8.5 in 10 in 4 in
\(V = l \cdot w \cdot h\)
\(V = 8.5\text{ in} \times 4\text{ in} \times 10\text{ in}\)
\(V = 34\text{ in}^2 \times 10\text{ in} = \mathbf{340\text{ in}^3}\)
Formula substitute: \(8.5 \times 4 \times 10\)
Answer: \(340\text{ in}^3\)
Prism Power Math Labs • ANSWER KEY Page 1 of 2
PRISM POWER: VOLUME EXPLORATIONS
Teacher Answer Key
LEVEL 2
Triangular Treks
4 Find the volume of the triangular prism. First calculate the area of the triangular base:
6 cm 4 cm 10 cm
\(B = \frac{1}{2} \cdot b \cdot h = \frac{1}{2} \times 6 \times 4 = \mathbf{12\text{ cm}^2}\)
\(V = B \cdot H\)
\(V = 12\text{ cm}^2 \times 10\text{ cm} = \mathbf{120\text{ cm}^3}\)
Base Area = \(12\text{ cm}^2\) | Height/Length = \(10\text{ cm}\)
Answer: \(120\text{ cm}^3\)
5 Determine the volume of this heavy metal triangular block:
8 in 5 in 12 in
