Question

1. there are several different measurements used for density. if you have a substance with a density of 2.0 g/cm³, what would the density be in pounds per cubic inch? (1 kg is equal to 2.2 pounds and 1 inch is equal to 2.54 cm)

Explanation:

Step1: Convert grams to pounds

We know that 1 kg = 1000 g and 1 kg = 2.2 pounds. So 1 g=$\frac{2.2}{1000}$ pounds.

Step2: Convert cubic - centimeters to cubic - inches

Since 1 inch = 2.54 cm, then 1 $cm=\frac{1}{2.54}$ inches and 1 $cm^{3}=(\frac{1}{2.54})^{3}$ $in^{3}$.

Step3: Calculate the new density

The original density is 2.0 g/$cm^{3}$. Substitute the conversion factors:
\[

$$\begin{align*} \text{Density}&=2.0\times\frac{\frac{2.2}{1000}\text{ pounds}}{(\frac{1}{2.54})^{3}\text{ in}^{3}}\\ &=2.0\times\frac{2.2}{1000}\times(2.54)^{3}\text{ pounds/in}^{3}\\ &=2.0\times\frac{2.2}{1000}\times16.387064\text{ pounds/in}^{3}\\ &=\frac{2.0\times2.2\times16.387064}{1000}\text{ pounds/in}^{3}\\ &=\frac{72.1030816}{1000}\text{ pounds/in}^{3}\\ & = 0.072\text{ pounds/in}^{3} \end{align*}$$

\]

Answer:

0.072 pounds per cubic inch