# 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.

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 $3$ .

$\begin{array}{l}A={\left(3\right)}^{2}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=9\end{array}$

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 |

$1{\text{yd}}^{2}=9{\text{ft}}^{2}$ | $1{\text{m}}^{2}=10,000{\text{cm}}^{2}$ |

$1{\text{ft}}^{2}=144{\text{in}}^{2}$ | $1{\text{cm}}^{2}=100{\text{mm}}^{2}$ |

### Volume

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

**
Example 2:
**

Convert one cubic foot to cubic inches.

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, $V=bwh$ , to convert cubic units.

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

$\begin{array}{l}V=\left(12\right)\left(12\right)\left(12\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=1,728\end{array}$

So, $1$ cubic foot is equal to $\mathrm{1,728}$ cubic inches.

### Common conversions for cubic units

The table gives several common measurement conversions for cubic units.

Customary Units | Metric Units |

$1{\text{yd}}^{3}=27{\text{ft}}^{3}$ | $1{\text{m}}^{3}=1,000,000{\text{cm}}^{3}$ |

$1{\text{ft}}^{3}=1,728{\text{in}}^{3}$ | $1{\text{cm}}^{3}=1,000{\text{mm}}^{3}$ |

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. ( $1\text{mL}\approx 1\text{g}$ )

**
Note:
**

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

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