Lesson 5: Volume Formulas and Equivalent Expressions

Property

We use cubic units to measure the volume or amount of space inside a three-dimensional object. For a box with dimensions length $l$, width $w$, and height $h$, the volume is found by multiplying the three dimensions.

Examples

• An aquarium is 3 feet long, 1.5 feet wide, and 2 feet tall. Its volume is $3 \times 1.5 \times 2 = 9$ cubic feet.

• A shoebox has dimensions of 14 inches by 8 inches by 5 inches. Its volume is $14 \times 8 \times 5 = 560$ cubic inches.

Property

The volume ($V$) of a rectangular prism is the area of its base ($B$) multiplied by its height ($h$). Since the base is a rectangle, its area is found by multiplying its length ($l$) and width ($w$).

Property

The volume of a prism is the product of the height by the area of the base.
That is, if the area of the base is $B$ and the height is $h$, volume is $V = Bh$.

Examples

• A rectangular prism with a base of $5 \text{ cm} \times 6 \text{ cm}$ and a height of $12 \text{ cm}$ has a volume of $V = (5 \times 6) \times 12 = 360 \text{ cm}^3$.

• A triangular prism has a base area of $30 \text{ in}^2$ and a height of $7 \text{ in}$. Its volume is $V = 30 \times 7 = 210 \text{ in}^3$.