Measurement - Volume of Cubes and Cuboids (Rectangular Prisms)

Volume represents the total amount of three-dimensional space an object occupies. To visualize this, imagine filling a hollow container with unit cubes (cubes with a side length of $1$ unit); the volume is the total count of those cubes required to fill the container completely.

A rectangular prism, also known as a cuboid, is a 3D shape with six rectangular faces. It is defined by three dimensions: length ($l$), width ($w$), and height ($h$). Visually, the length and width form the flat rectangular base, while the height determines how many layers of that base are stacked vertically.

A cube is a specific type of rectangular prism where all three dimensions (length, width, and height) are equal. Because every face is an identical square, we refer to the dimension simply as the side or edge length ($s$).

Units of volume are always expressed in 'cubic' units, such as $mm^3$, $cm^3$, or $m^3$. This '3' exponent indicates that the measurement accounts for three dimensions (length, width, and height) being multiplied together.

The volume of a prism can be understood by calculating the 'Base Area' first. If you calculate the area of the bottom face ($l \times w$), you are finding out how many unit squares cover the floor of the prism. Multiplying this area by the height ($h$) tells you how many of those layers fill the entire height.

Capacity is the volume of fluid a container can hold. In the metric system, there is a direct relationship between solid volume and liquid capacity: $1 cm^3$ is equal to $1 ml$, and $1000 cm^3$ is equal to $1 L$.

To find a missing dimension when the volume is known, you can rearrange the formula. For instance, if you know the volume and the base area, you can find the height by dividing the volume by the base area: $h = \frac{V}{l \times w}$.