Volume of rectangular prisms (cubic cm & m)
Theory
The volume of a rectangular prism is how many unit cubes fill it: length times width times height, \(V = l \times w \times h\). Volume is measured in cubic units such as cm\(^3\).
A rectangular prism is a box shape. Its volume is the amount of space inside it.
Volume is length times width times height: \(V = l \times w \times h\). It equals the number of unit cubes that fill the box.
One layer holds \(l \times w\) cubes, and there are \(h\) layers. Volume is measured in cubic units, such as cm\(^3\).
| Length | Width | Height | Volume |
|---|---|---|---|
| \(4\) | \(2\) | \(3\) | \(24\) |
| \(5\) | \(3\) | \(2\) | \(30\) |
How to find the volume of a rectangular prism
- Find the length, width and height.
- Multiply all three together.
- Write the answer in cubic units.
| \(V\) | \(=\) | \(4 \times 2 \times 3 = 24\) |
\(24\) cubes.
| \(V\) | \(=\) | \(5 \times 3 \times 2 = 30\) |
Volume \(= 30\) cm\(^3\).
| \(V\) | \(=\) | \(12 \times 4 = 48\) |
\(48\) cubic units.
| \(V\) | \(=\) | \(3 \times 3 \times 3 = 27\) |
Volume \(= 27\) cm\(^3\).
Common pitfalls
Frequently asked questions
What is the volume of a rectangular prism?
Length times width times height, \(V = l \times w \times h\). A box \(5\) by \(3\) by \(2\) has a volume of \(30\) cubic units.
Why do you multiply three numbers?
One layer holds length times width cubes, and there are height layers, so you multiply all three.
What units is volume measured in?
Cubic units, such as cubic centimetres (cm\(^3\)), because three lengths are multiplied.
How do you count cubes in a prism?
Count one layer, then multiply by the number of layers. Remember the cubes hidden at the back.