Taking into account the definition of density and change of units, if a container is strong enough to hold 62.0 pounds (lb) of gasoline, you can put 10.3184 gallons in there.
First you must know that 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 the relationship between the weight (mass) of a substance and the volume it occupies (that same 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]
On the other side, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, where a, b and c are known values and x is the value to be calculated:
a ⇒ b
c ⇒ x
So, [tex]x=\frac{cxb}{a}[/tex]
The direct rule of three is the rule applied in this case where there is a change of units. To perform conversion of units from pounds to grams, you must first know that 1 lb = 453.59 g. So, if 453.59 g is 1 lb, how many grams equals 62 lb?
[tex]mass= \frac{62 lbx453.59 g}{1 lb}[/tex]
Solving:
mass= 28122.58 grams
Then, you know:
Replacing in the definition of density:
[tex]0.720\frac{g}{cm^{3} }=\frac{28122.58 g}{volume}[/tex]
Solving:
volume×0.720 [tex]\frac{g}{cm^{3} }[/tex]= 28122.58 g
[tex]volume=\frac{28122.58 g}{0.720\frac{g}{cm^{3} }}[/tex]
volume= 39059.14 cm³= 39059.14 mL= 39.05914 L (being 1 cm³= 1 mL= 0.001 L)
Now, to perform conversion of units from L to qt, you must first know that 1 qt = 0.94635 L. So, if 1 qt is 0.94635 L, how many qt equals 39.05914 L?
[tex]volume= \frac{39.05914 Lx1 qt}{0.94635 L}[/tex]
Solving:
volume= 41.2735 qt
Finally, to perform conversion of units from qt to gal, you must first know that 1 gal = 4.0000 qt. So, if 1 gal is 4 qt, how many gal equals 41.2735 qt?
[tex]volume= \frac{41.2735 qtx1 gal}{4 qt}[/tex]
Solving:
volume= 10.3184 gal
In summary, if a container is strong enough to hold 62.0 pounds (lb) of gasoline, you can put 10.3184 gallons in there.
Learn more about density:
