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Answer :
Final Answer:
This conversion is obtained by first converting grams to pounds and then cubic centimeters to cubic feet. Thus the correct option is C. 1.177 * [tex]10^{-6}[/tex] [tex]{lb/ft}^3 \).[/tex]
Explanation:
To convert the density of the unknown solid from grams per cubic centimeter (g/[tex]cm^3[/tex]) to pounds per cubic foot ([tex]lb/ft^3[/tex]), we follow these steps:
Convert grams to pounds:
Given that[tex]\( 1 \, \text{g} = 0.00220462 \, \text{lb} \)[/tex], we multiply the density of the unknown solid (15.1 g/[tex]cm^3[/tex]) by this conversion factor:
[tex]\[ 15.1 \, \text{g/cm}^3 \times 0.00220462 \, \text{lb/g} = 0.033306 \, \text{lb/cm}^3 \][/tex]
Convert cubic centimeters to cubic feet:
Given that[tex]\( 1 \, \text{cm}^3 = 0.0000353147 \, \text{ft}^3 \)[/tex], we multiply the result from Step 1 by this conversion factor:
[tex]\[ 0.033306 \, \text{lb/cm}^3 \times 0.0000353147 \, \text{ft}^3/\text{cm}^3 = 0.000001177 \, \text{lb/ft}^3 \][/tex]
Round to appropriate significant figures:
Rounding off the result from Step 2 to three significant figures, we get approximately 1.177 * [tex]10^{-6}[/tex] [tex]{lb/ft}^3 \).[/tex]
Thus the correct option is C. 1.177 * [tex]10^{-6}[/tex] [tex]{lb/ft}^3 \).[/tex]
The complete question is:
"The density of a sample of an unknown solid is 15.1 g/cm3. Convert this density to units of lb/ft3. You don't need to include units, but pay attention to significant figures!
Options:
A) 1.1 lb/ft3
B) 8.7 lb/ft3
C) 1.177 * [tex]10^{-6}[/tex] [tex]{lb/ft}^3 \).[/tex]
D) 240 lb/ft3"
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