Volume of Rectangular Prisms
Learn how to calculate the volume of rectangular prisms and cubes using length, width, and height.
Definition
The Volume Formula
- = length (how long)
- = width (how wide)
- = height (how tall)
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Worked Examples
A storage box has length 8 cm, width 5 cm, and height 4 cm. What is its volume?
Write the formula
→ Formula identified
Substitute the values
→ Values plugged in
Multiply length and width
→ Base area = 40 cm²
Multiply by height
→ cm³
Answer: The volume is cm³ (cubic centimeters)
Common Mistakes
Confusing volume with surface area
Why it's wrong: Volume measures space inside (cubic units), while surface area measures the outside covering (square units).
Correct: Volume uses multiplication of 3 dimensions: . Surface area adds up all 6 faces.
Forgetting cubic units
Why it's wrong: Volume is 3-dimensional, so the unit must also be cubed (cm³, m³, in³).
Correct: Always write the unit with a cube: 60 cm³, not 60 cm.
Mixing up measurements from different units
Why it's wrong: Multiplying centimeters by meters gives an incorrect result.
Correct: Convert all dimensions to the same unit first. If length is in meters and width in cm, convert one to match the other.
Interactive Visual
3D Shape Viewer
Faces
6
Edges
12
Vertices
8
Volume
V = lwh
60 units³
Surface Area
SA = 2(lw + lh + wh)
94 units²
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
16 problemsWhat is the formula for the volume of a rectangular prism?
Why It Matters
- Packing: How many toys fit in a box?
- Shipping: What size box do you need for your package?
- Aquariums: How much water does a fish tank hold?
- Construction: How much concrete is needed to fill a foundation?
- Storage: Will this refrigerator fit in the kitchen space?
Real World Applications
Shipping and Packaging
Companies calculate box volumes to determine shipping costs and how many items fit in a container.
Example:
A shipping box is 12 in × 8 in × 6 in. Its volume is cubic inches.
You need to ship books in a box measuring 15 cm × 10 cm × 20 cm. Each book is 15 cm × 10 cm × 2 cm.
How many books can fit in the box?
Step 1: Write the mathematical expression
First find the box volume, then the book volume, then divide:
Concrete for Construction
Builders calculate volume to order the right amount of concrete for foundations and slabs.
Example:
A foundation is 10 m × 8 m × 0.5 m. Volume = m³ of concrete needed.
A sidewalk needs to be 20 m long, 1.5 m wide, and 0.1 m thick.
How many cubic meters of concrete are needed?
Step 1: Write the mathematical expression
Calculate:
Key Takeaways
- 1Volume measures the space inside a 3D object in cubic units
- 2Formula for rectangular prism: (length × width × height)
- 3Formula for cube: (side cubed)
- 4Always include cubic units in your answer (cm³, m³, in³, ft³)
- 5To find a missing dimension, rearrange the formula and divide
Frequently Asked Questions
Glossary
- Volume
- The amount of space inside a 3D object, measured in cubic units
- Rectangular prism
- A 3D shape with 6 rectangular faces (also called a cuboid)
- Cube
- A rectangular prism where all edges have equal length
- Cubic units
- Units for measuring volume, like cm³, m³, or in³
- Dimensions
- The measurements of length, width, and height
Formula Card
Rectangular Prism
Volume equals length times width times height
Cube
Volume equals side cubed (s × s × s)