Q 1.2E - University Physics with Modern Physics

Question

Question: According to the label on a bottle of salad dressing, the volume of the contents is 0.473 liter (L). Using only the conversions 1 L = 1000 cm³ and 1 in. = 2.54 cm, express this volume in cubic inches.

 

Step-by-Step Solution

Answer

The volume in cubic inches is 27.86 in³.

Step 1: What is volume

There are many units to measure the volume of the container. Volume means measuring the amount of substance that can be contained by the container. It can also be called as the space occupied by the system. Some examples are litre, meter cube, centimetre cube etc.

Given data:

 $\begin{array}{l}1\text{\hspace{0.17em}L}=1000{\text{\hspace{0.17em}cm}}^3\\ 1\text{\hspace{0.17em}in}=2.54\text{\hspace{0.17em}cm}\end{array}$

Step 2: Converting volume in cm 3

The conversion of liter into cm³ is shown below,

 $\begin{array}{l}0.473\text{\hspace{0.17em}L}=0.473\text{\hspace{0.17em}L}\times \frac{1000{\text{\hspace{0.17em}cm}}^3}{1\text{\hspace{0.17em}L}}\\ 0.473\text{\hspace{0.17em}L}=473{\text{\hspace{0.17em}cm}}^3\end{array}$

Step 3: Converting volume in inch 3

The conversion of cm³ into inch³ is shown below,

$\begin{array}{l}0.473{\text{\hspace{0.17em}cm}}^3=473{\text{\hspace{0.17em}cm}}^3\times {\left(\frac{1\text{\hspace{0.17em}in}}{2.54\text{\hspace{0.17em}cm}}\right)}^3\\ 0.473{\text{\hspace{0.17em}cm}}^3=28.86{\text{\hspace{0.17em}in}}^3\end{array}$ 

 

Hence, the volume in cubic inches is 28.86 in³.