Convert Units of Area and Volume

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 $3$ .

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

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

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 $12$ .

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

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