Question

23 formula 5 points
convert 79.73 lb/ft³ to g/cm³. solve to 4 significant figures.
useful conversion factors:
1 kg = 2.2046 lb
2.54 cm = 1 in (exact)
answer

Explanation:

Step1: Convert pounds to grams

First, convert pounds to kilograms and then kilograms to grams. Since $1\ kg = 2.2046\ lb$, then $1\ lb=\frac{1}{2.2046}\ kg$. And since $1\ kg = 1000\ g$, so $1\ lb=\frac{1000}{2.2046}\ g$.
$79.73\ lb=\ 79.73\times\frac{1000}{2.2046}\ g$.

Step2: Convert cubic - feet to cubic - centimeters

We know that $1\ ft = 12\ in$ and $1\ in=2.54\ cm$, so $1\ ft=(12\times2.54)\ cm = 30.48\ cm$. Then $1\ ft^{3}=(30.48)^{3}\ cm^{3}$.

Step3: Calculate the conversion

The density $d = 79.73\frac{lb}{ft^{3}}$. Substitute the conversion factors:
\[

$$\begin{align*} d&=79.73\times\frac{\frac{1000}{2.2046}\ g}{(30.48)^{3}\ cm^{3}}\\ &=79.73\times\frac{1000}{2.2046\times(30.48)^{3}}\frac{g}{cm^{3}}\\ &=79.73\times\frac{1000}{2.2046\times28316.846592}\frac{g}{cm^{3}}\\ &=79.73\times\frac{1000}{62208.23399}\frac{g}{cm^{3}}\\ &=79.73\times0.016076\frac{g}{cm^{3}}\\ & = 1.283\frac{g}{cm^{3}} \end{align*}$$

\]

Answer:

$1.283\ g/cm^{3}$