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Convert Units of Area and Volume

The objective of the lesson is to convert units of measure between dimensions including area and volume .

Area:

The area is measured in square units (unit ^$2$ ).

Example 1:

Convert one square yard to square feet.

Math diagram

A square yard is a square with a side length of one yard.

We know that, $1$ yard = $3$ feet.

So, $1$ square yard is a square with side length $3$ feet.

You can use the formula for the area of a square, $A = s^{2}$ , to convert square units.

Since $1$ yard = $3$ feet, substitute $s$ by $3$ .

$\begin{array}{l} A = {(3)}^{2} \\ = 9 \end{array}$

So, $1$ square yard is equal to $9$ square feet.

Common conversions for Square Units

The table gives several common measurement conversions for square units.

Customary Units	Metric Units
$1 {yd}^{2} = 9 {ft}^{2}$	$1 m^{2} = 10, 000 {cm}^{2}$
$1 {ft}^{2} = 144 {in}^{2}$	$1 {cm}^{2} = 100 {mm}^{2}$

Volume

The volume is measured in cubic units (unit ^$3$ ).

Example 2:

Convert one cubic foot to cubic inches.

Math diagram

A cubic foot is a cube with a side length of one foot.

We know that, $1$ foot = $12$ inches.

So, $1$ cubic foot is a cube with side length $12$ inches.

You can use the formula for the volume of a prism, $V = b w h$ , to convert cubic units.

Since $1$ foot = $12$ inches, replace $b$ , $w$ , and $h$ with $12$ .

$\begin{array}{l} V = (12) (12) (12) \\ = 1, 728 \end{array}$

So, $1$ cubic foot is equal to $1,728$ cubic inches.

Common conversions for cubic units

The table gives several common measurement conversions for cubic units.

Customary Units	Metric Units
$1 {yd}^{3} = 27 {ft}^{3}$	$1 m^{3} = 1, 000, 000 {cm}^{3}$
$1 {ft}^{3} = 1, 728 {in}^{3}$	$1 {cm}^{3} = 1, 000 {mm}^{3}$

The metric system also relates length, mass, and capacity.

$1$ milliliter has the same volume as $1$ cubic centimeter. ( $1$ mL = $1$ cc)

$1$ milliliter of water is approximately $1$ gram. ( $1 mL \approx 1 g$ )

Note:

A length is measured in units , area is measured in square units $(unit \times unit = {unit}^{2})$ , and volume is measured in cubic units $(unit \times unit \times unit = {unit}^{3})$ .