Unit 10 · Standard 6.G.2
Volume of Rectangular Prisms
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
A box 2 × 1.5 × 1 = 3 ft³ — it holds 3 cubic feet of stuff
Volume
How much space is inside a solid shape.
A tissue box, a fish tank, a brick — all rectangular prisms
Rectangular prism
A solid box shape with six flat rectangle sides.
1 ft³ = a cube that is 1 foot on every edge
Cubic units
The units used to measure space inside, like cubic inches.
A box with dimensions 4 × 3 × 2 means l = 4, w = 3, h = 2
Dimensions
How long, how wide, and how tall a shape is.
Cut a cereal box along its edges, unfold it flat — that is the net
Net
A flat shape that folds up into a solid.
If the base is 6 × 4 = 24 cm² and h = 3, then V = 24 × 3 = 72 cm³
Base area
The area of the bottom of a solid. Volume = base area × height.
Key Ideas & Notes
- Your class is building a time capsule to bury on school grounds.
- The capsule is a rectangular prism that is 2 feet long, 1.5 feet wide, and 1 foot tall.
- You need to figure out how much stuff can fit inside — that means calculating the volume!
- Calculate the volume of each possible time capsule design. Use V = l × w × h.
Think About It
- What are the three measurements of the time capsule?
- What does volume measure — length, area, or space inside?
- How is volume different from area?
My Notes
Guided Examples
Example 1
What is the volume of a rectangular prism with l = 4 in, w = 3 in, h = 5 in?
Solution: V = l × w × h = 4 × 3 × 5 = 60 cubic inches.
Answer: A. 60 in³
Example 2
A box has a volume of 36 cm³. Its length is 6 cm and width is 3 cm. What is the height?
Solution: V = l × w × h → 36 = 6 × 3 × h → 36 = 18h → h = 2 cm.
Answer: A. 2 cm
Example 3
How is volume different from area?
Solution: Volume measures the space inside a 3D shape (cubic units like in³). Area measures a flat 2D surface (square units like in²).
Answer: A. Volume measures 3D space (cubic units); area measures 2D surface (square units)
Write About the Math The Writing Revolution
I can explain my work using the words volume, rectangular prism, dimensions, and base area.
1. Kernel Sentence subject + verb
Model: Volume is how much space is inside a solid shape.Volumen es cuánto espacio hay dentro de una figura sólida.
Write a kernel sentence about volume. Use a subject and a verb.Escribe una oración base sobre volumen. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Volume matters in mathVolumen importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Volume matters in math because ___.Volumen importa en matemáticas porque ___.
Volume matters in math, but ___.Volumen importa en matemáticas, pero ___.
Volume matters in math, so ___.Volumen importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about volume.Di un hecho verdadero sobre volume.
Volume ___.
Ask a question about volume.Haz una pregunta sobre volume.
How does ___ ?¿Cómo ___ ?
Show excitement about volume.Muestra entusiasmo sobre volume.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with volume.Dile a un compañero qué hacer con volume.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I multiplied ___ by ___ by ___.Multipliqué ___ por ___ por ___.
The volume is ___.El volumen es ___.
I would use this to ___.Usaría esto para ___.
Try It
Solve on your own. Check the answer key when you are done.
1. How is volume different from area?
- Volume measures 3D space (cubic units); area measures 2D surface (square units)
- Volume uses square units; area uses cubic units
- Volume only applies to cubes; area applies to all shapes
- There is no difference
2. Two boxes: Box A is 10 × 5 × 4 inches. Box B is 8 × 6 × 5 inches. Which has more volume and by how much?
- Box B by 40 in³
- Box A by 40 in³
- Box B by 60 in³
- They're equal
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A toy company ships action figures in boxes that are 4 × 3 × 6 inches. A shipping crate is 24 × 12 × 18 inches. How many action figure boxes fit in the crate? Explain your reasoning step by step.
Sentence starter: Each toy box has a volume of ___ in³. The crate has a volume of ___ in³. I can fit ___ boxes because ___. I checked by ___.
Reflect — Exit Ticket
A rectangular prism has l = 7 ft, w = 2 ft, h = 3 ft. What is the volume?
- 42 ft³
- 24 ft³
- 42 ft²
- 12 ft³
Answer Key & Teacher Guide
- Try It 1: A. Volume measures 3D space (cubic units); area measures 2D surface (square units) — Volume measures the space inside a 3D shape (cubic units like in³). Area measures a flat 2D surface (square units like in²).
- Try It 2: A. Box B by 40 in³ — Box A: 10 × 5 × 4 = 200 in³. Box B: 8 × 6 × 5 = 240 in³. Box B is bigger by 40 in³.
- Exit Ticket: A. 42 ft³ — V = 7 × 2 × 3 = 42 cubic feet. Remember: volume uses cubic units (ft³).
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Volume is how much space is inside a solid shape.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).