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 cm³=$(\frac{1}{2.54})^3$ cubic inches.

Step3: Calculate the new density

The original density is 2.0 g/cm³. Substitute the conversion factors into the density formula.
The new density $d$ is:
\[

$$\begin{align*} d&=2.0\times\frac{\frac{2.2}{1000}}{(\frac{1}{2.54})^3}\text{ pounds per cubic inch}\\ &=2.0\times\frac{2.2}{1000}\times(2.54)^3\text{ pounds per cubic inch}\\ &=2.0\times\frac{2.2}{1000}\times16.387064\text{ pounds per cubic inch}\\ &=2.0\times2.2\times0.016387064\text{ pounds per cubic inch}\\ & = 0.0721030816\text{ pounds per cubic inch}\approx0.072\text{ pounds per cubic inch} \end{align*}$$

\]

Answer:

0.072 pounds per cubic inch