Lesson 8: Volume of Rectangular Prisms

Property

To find the volume of a real-world object shaped like a rectangular prism, multiply its length, width, and height. The dimensions can be whole numbers, fractions, or mixed numbers.

Property

When the volume and two dimensions of a rectangular prism are known, the missing dimension can be found by rearranging the volume formula: $V = lwh$.
Solve for the unknown dimension by dividing the volume by the product of the known dimensions.

Examples

Property

For a cube with side length $s$:

• Volume: $V = s^3$
• Surface Area: $SA = 6s^2$

Examples

• A cube with side length $s = 4$ cm has a volume of $V = 4^3 = 64$ cm$^3$ and a surface area of $SA = 6 \cdot 4^2 = 6 \cdot 16 = 96$ cm$^2$.
• A cube with side length $s = 10$ ft has a volume of $V = 10^3 = 1000$ ft$^3$ and a surface area of $SA = 6 \cdot 10^2 = 6 \cdot 100 = 600$ ft$^2$.

Explanation

The volume of a cube is found by cubing its side length, which means multiplying the side length by itself three times. The surface area is the total area of all its faces. Since a cube has 6 identical square faces, you find the area of one face by squaring the side length ($s^2$) and then multiplying it by 6.