Definition
Volume
Volume is the amount of three-dimensional space a solid or region occupies.
What it means
Think about packing a solid with unit cubes, with no gaps or overlaps. The number of cubes tells its volume. For a rectangular box, the layers of cubes can be counted by multiplying length, width, and height.
Remember it
Ask how many unit cubes would fill the space.
Example
A box is 4 cm long, 3 cm wide, and 2 cm high. One layer holds 4 × 3 = 12 unit cubes, and there are 2 layers, so the volume is 12 × 2 = 24 cm³.
Watch for
A flat rectangle has area, not volume; volume needs three dimensions.
Common mix-up
Capacity tells how much a container can hold. Volume tells how much three-dimensional space a region occupies.
Exact meaning
Volume measures the three-dimensional space occupied by a solid or bounded region. It is measured in cubic units; a rectangular prism with side lengths l, w, and h has volume l × w × h.