Taking into account the definition of density, the volume of a full tank car which contains 3.22×10⁴ kg of acetone is 41.02 m³.
Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space.
In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance.
Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:
[tex]density=\frac{mass}{volume}[/tex]
From this expression it can be deduced that density is inversely proportional to volume: the smaller the volume occupied by a given mass, the higher the density.
In this case, you know that:
Replacing in the definition of density:
[tex]0.785 \frac{g}{cm^{3} }=\frac{32,200,000 g}{volume}[/tex]
Solving:
volume×0.785[tex]\frac{g}{cm^{3} }[/tex]= 32,200,000 g
volume=[tex]\frac{32,200,000 g}{0.785 \frac{g}{cm^{3} }}[/tex]
volume= 41,019,108.28 cm³= 41.01910828 m³≅ 41.02 m³ (being 1 m³ = 1000000 cm³)
In summary, the volume of a full tank car which contains 3.22×10⁴ kg of acetone is 41.02 m³.
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