Volume of Rectangular Prisms

Volume is the amount of space inside a three-dimensional (3D) figure. Imagine filling a box with water or sand—the amount it holds is its volume. We measure volume in cubic units, such as cubic centimeters ($\text{cm}^3$) or cubic inches ($\text{in}^3$).

Finding Volume by Counting Cubes

One way to understand volume is by packing a shape with unit cubes (cubes where every side is $1$ unit long).

For example, how many unit cubes fill a box that is $6 \times 4 \times 3$?

1. First, find the number of cubes in the bottom layer: $6 \times 4 = 24$ cubes.
2. Next, look at the height. Since the height is $3$, there are $3$ layers of $24$ cubes.
3. Multiply the cubes in the base layer by the number of layers: $24 \times 3 = 72$ unit cubes.

The Volume Formula

Instead of counting cubes every time, you can use a simple formula for any rectangular prism: $V = l \times w \times h$ Where $V$ is volume, $l$ is length, $w$ is width, and $h$ is height.

Example: Find the volume of a rectangular prism that is $5\text{ cm}$ long, $3\text{ cm}$ wide, and $4\text{ cm}$ high. $V = 5 \times 3 \times 4$ $V = 60\text{ cm}^3$

Volume of Composite Solids

Sometimes you will see a shape made of two connected rectangular prisms, like an L-shaped solid. To find the volume of these composite solids:

1. Split the shape into two non-overlapping rectangular prisms.
2. Calculate the volume of each prism separately using the formula $V = l \times w \times h$.
3. Add the two volumes together to get the total volume.

If Prism A has a volume of $20\text{ cm}^3$ and Prism B has a volume of $30\text{ cm}^3$, the total volume is simply $20 + 30 = 50\text{ cm}^3$.