Q41P - Fundamentals Of Physics

Question

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${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }{\mathbf{m}}^{\mathbf{3}}}$?

Step-by-Step Solution

Answer

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

Step 1: Given data

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 ${}^{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{ }{\mathbf{m}}^{\mathbf{3}}}$.

Step 2: Understanding the conversion factor

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.

Step 3: Determination of the volume of a cord of wood

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${}^{\mathbf{128}\mathbf{ }\mathbf{ft}}$.

Step 4: Determination of the number of cords

Volume has to be converted into cubic meters.

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

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

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 ${}^{\mathbf{0}\mathbf{.}\mathbf{3}\mathbf{ }\mathbf{cord}}$ .