To determine the density of glycerin in pounds per cubic foot given its density in grams per cubic centimeter, we need to follow these steps:
1. Convert density from grams per cubic centimeter to pounds per cubic centimeter:
The density of glycerin is [tex]\(1.26 \frac{\text{grams}}{\text{cm}^3}\)[/tex].
We know the conversion rate is [tex]\(1 \text{ pound} = 454 \text{ grams}\)[/tex].
Therefore, the density in pounds per cubic centimeter is calculated as:
[tex]\[
\frac{1.26 \text{ grams}}{\text{cm}^3} \times \frac{1 \text{ pound}}{454 \text{ grams}} = 0.002775330396475771 \frac{\text{pounds}}{\text{cm}^3}
\][/tex]
2. Convert density from pounds per cubic centimeter to pounds per cubic foot:
We know the conversion rate is [tex]\(1 \text{ cubic foot} = 28,317 \text{ cubic centimeters}\)[/tex].
Therefore, the density in pounds per cubic foot is calculated as:
[tex]\[
0.002775330396475771 \frac{\text{pounds}}{\text{cm}^3} \times 28,317 \text{ cm}^3 = 78.59 \frac{\text{pounds}}{\text{foot}^3}
\][/tex]
3. Express the answer to correct significant figures:
The given density of glycerin ([tex]\(1.26 \frac{\text{grams}}{\text{cm}^3}\)[/tex]) has 3 significant figures. The final answer should be rounded to match this.
Therefore, the density of glycerin is [tex]\(78.59 \frac{\text{pounds}}{\text{foot}^3}\)[/tex].
