Volume of 3D Shapes
Grade 6 · Math · Study Guide
Learn to find the volume of rectangular prisms and other 3D figures using formulas.
Volume measures how much 3D space an object takes up — how much it can hold inside. We measure volume in cubic units: cm³, in³, m³. Think of filling a box with tiny unit cubes — the number of cubes needed is the volume.
For a rectangular prism, the formula is simple: V = l × w × h (length times width times height). A fish tank that is 30 cm long, 15 cm wide, and 20 cm tall has a volume of 30 × 15 × 20 = 9,000 cm³. Since 1 liter = 1,000 cm³, that tank holds 9 liters of water.
You can also think of volume as base area times height: V = B × h, where B is the area of the base. For a rectangular prism, B = l × w, so V = lw × h = lwh. This formula works for ALL prisms and cylinders, not just rectangular ones.
Volume is different from surface area: surface area is what's on the outside, volume is what's on the inside. A big hollow box and a small solid cube might have similar surface areas but very different volumes.
| Shape | Formula | Example |
|---|---|---|
| Rectangular Prism | V = l × w × h | 4×3×5 = 60 cm³ |
| Cube | V = s³ | 4³ = 64 cm³ |
| Any Prism | V = B × h | B = base area, h = height |
Key terms
- Volume
- The amount of 3D space inside a solid, measured in cubic units
- Cubic Unit
- A unit of volume — a cube with side length 1 (like 1 cm³)
- Rectangular Prism
- A 3D solid with 6 rectangular faces and right angles at all corners
- Base Area (B)
- The area of the bottom face of a 3D solid
Flashcards
- Volume
- 3D space inside a solid — measured in cubic units (cm³, in³, m³)
- Rectangular prism volume
- V = l × w × h
- Cube volume
- V = s³ (side cubed)
- V = B × h
- Volume = base area × height — works for any prism
- Cubic units
- Units for volume: cm³, in³, ft³ — always cubed, not squared
- Difference: volume vs surface area
- Volume = inside space (cubic units); Surface area = outside covering (square units)
Practice questions
A rectangular prism has length 6 cm, width 4 cm, and height 5 cm. What is its volume?
- 120 cm³
- 74 cm²
- 60 cm³
- 120 cm²
Show answer
Answer: 120 cm³
V = 6 × 4 × 5 = 120 cm³. Volume uses cubic units, not square units.
What is the volume of a cube with side length 7 in?
- 343 in³
- 294 in²
- 49 in³
- 42 in³
Show answer
Answer: 343 in³
V = s³ = 7³ = 7×7×7 = 343 in³.
Volume is measured in square units.
Show answer
Answer: False
Volume is measured in CUBIC units (cm³, in³). Square units are for area.
The formula for volume of a rectangular prism is V = l × w × ___.
Show answer
Answer: h
V = l × w × h — all three dimensions are multiplied together for a rectangular prism.
A box has a base area of 24 in² and a height of 5 in. What is its volume?
- 120 in³
- 29 in³
- 120 in²
- 24 in³
Show answer
Answer: 120 in³
V = B × h = 24 × 5 = 120 in³.
Fun facts
- The Great Pyramid of Giza has a volume of about 2.6 million cubic meters — enough to fill over 1 million average-sized swimming pools.
- A standard shipping container has a volume of about 33 cubic meters (33,000 liters). Over 800 million shipping containers move goods around the world each year!
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