Volume of Rectangular Prisms
Grade 5 · Math · Study Guide
Learn to find the volume of rectangular prisms using the formula V = l × w × h.
Volume measures how much 3-dimensional space an object occupies and is expressed in cubic units (such as cubic centimeters or cubic inches). A rectangular prism is a box-shaped figure with 6 rectangular faces.
The formula for volume is V = l × w × h, where l is length, w is width, and h is height. You can also think of it as the area of the base (l × w) multiplied by the height.
When all measurements are in the same unit, the volume unit is that unit cubed. For example, if length, width, and height are in centimeters, the volume is in cubic centimeters (cm³).
| Length | Width | Height | Volume |
|---|---|---|---|
| 4 cm | 3 cm | 2 cm | 4 × 3 × 2 = 24 cm³ |
| 5 in | 5 in | 5 in | 5 × 5 × 5 = 125 in³ |
| 10 m | 2 m | 3 m | 10 × 2 × 3 = 60 m³ |
| Object | Approximate Dimensions | Volume |
|---|---|---|
| Shoebox | 30 cm × 15 cm × 12 cm | 5,400 cm³ |
| Aquarium | 60 cm × 30 cm × 40 cm | 72,000 cm³ |
| Brick | 20 cm × 10 cm × 6 cm | 1,200 cm³ |
Key terms
- Volume
- The amount of 3D space inside a solid figure, measured in cubic units.
- Rectangular Prism
- A 3D solid with 6 rectangular faces, like a cereal box or a brick.
- Cubic Unit
- A unit of volume, such as cm³ or in³, representing a cube with sides of 1 unit.
- V = l × w × h
- The volume formula: multiply length, width, and height together.
Practice questions
What is the volume of a box with length 6 cm, width 4 cm, and height 3 cm?
- 13 cm³
- 72 cm³
- 48 cm³
- 36 cm³
Show answer
Answer: 72 cm³
V = 6 × 4 × 3 = 72 cm³.
A cube has sides of 5 inches. What is its volume?
- 15 in³
- 125 in³
- 25 in³
- 75 in³
Show answer
Answer: 125 in³
V = 5 × 5 × 5 = 125 in³.
A rectangular prism has l=8, w=3, h=2. Volume = ___
Show answer
Answer: 48
V = 8 × 3 × 2 = 48 cubic units.
Volume = 60 cm³, length = 5 cm, width = 4 cm. Height = ___
Show answer
Answer: 3 cm
V = l × w × h → 60 = 5 × 4 × h → 60 = 20h → h = 3 cm.
A fish tank is 50 cm long, 25 cm wide, and 30 cm tall. What is its volume?
- 37,500 cm³
- 3,750 cm³
- 375,000 cm³
- 1,500 cm³
Show answer
Answer: 37,500 cm³
V = 50 × 25 × 30 = 37,500 cm³.
Fun facts
- A cubic meter of water weighs exactly 1,000 kilograms (one metric ton)!
- The Great Pyramid of Giza has an estimated volume of about 2.5 million cubic meters.
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