A cord is a volume of cut wood equal to a stack 8 ft long, 4 ft wide, and 4 ft high. How many cords are in${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{}{\mathbf{m}}^{\mathbf{3}}}$?

Length is equal to${}^{\mathbf{8}\mathbf{}\mathbf{ft}}$.

Width is equal to${}^{\mathbf{4}\mathbf{}\mathbf{ft}}$,

Height is equal to${}^{\mathbf{4}\mathbf{}\mathbf{ft}}$.

The volume is role="math" localid="1654341559271" ${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{}{\mathbf{m}}^{\mathbf{3}}}$.

The given dimension of the cord of wood is in feet. By using the conversion factor, the volume of the cord is converted into meters.

The conversion factors are as below:

$\mathbf{1}\mathbf{}\mathbf{inch}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0254}\mathbf{}\mathbf{m}$

$\mathbf{1}\mathbf{}\mathbf{ft}\mathbf{=}\mathbf{12}\mathbf{}\mathbf{inch}$

$\mathbf{1}\mathbf{}\mathbf{ft}\mathbf{=}\mathbf{12}\mathbf{}\mathbf{inch}\mathbf{\times }\frac{\mathbf{0}\mathbf{.}\mathbf{0254}\mathbf{}\mathbf{m}}{\mathbf{}\mathbf{inch}}$

$\mathbf{1}\mathbf{}\mathbf{ft}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{3048}\mathbf{}\mathbf{m}$

The volume of a cord of wood is,

$$\begin{gathered} \mathbf{V}\mathbf{=}\mathbf{Lenght}\mathbf{\times }\mathbf{Breadth}\mathbf{\times }\mathbf{Height} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{8}\mathbf{}\mathbf{ft}\mathbf{\times }\mathbf{}\mathbf{4}\mathbf{}\mathbf{ft}\mathbf{\times }\mathbf{}\mathbf{4}\mathbf{}\mathbf{ft} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{128}\mathbf{}{\mathbf{ft}}^{\mathbf{3}} \end{gathered}$$

Thus, the volume of a cord of wood is${}^{\mathbf{128}\mathbf{}\mathbf{ft}}$.

Volume has to be converted into cubic meters.

By using conversion factor, the volume of a cord of wood comes to 128

$$\begin{gathered} \mathbf{128}\mathbf{}{\mathbf{ft}}^{\mathbf{3}\mathbf{}}\mathbf{=}\mathbf{}\mathbf{128}\mathbf{}{\mathbf{ft}}^{\mathbf{3}}\mathbf{}\mathbf{\times }\frac{{\left(0.3048m\right)}^{\mathbf{3}}}{\mathbf{1}\mathbf{}{\mathbf{ft}}^{\mathbf{3}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{625}\mathbf{}{\mathbf{m}}^{\mathbf{3}} \end{gathered}$$

So, volume of one cord of wood is${}^{\mathbf{3}\mathbf{.}\mathbf{625}\mathbf{}{\mathbf{meter}}^{\mathbf{3}}}$

Therefore, ${}^{\mathbf{1}\mathbf{}{\mathbf{m}}^{\mathbf{3}}}$of wood corresponds to,

$$\begin{gathered} \mathbf{1}\mathbf{}{\mathbf{m}}^{\mathbf{3}}\mathbf{}\mathbf{wood}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{\mathbf{3}\mathbf{.}\mathbf{62}}\mathbf{}\mathbf{cord} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{276}\mathbf{}\mathbf{cord} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\approx }\mathbf{}\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{cord} \end{gathered}$$

Thus, the number of cords in ${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{}{\mathbf{m}}^{\mathbf{3}}}$is ${}^{\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{cord}}$.