Question

The unit for density found in many density tables is kg/m3. At a certain temperature, the gasoline you pump into you car’s gas tank has a density of 732.22 kg/m3. If your tank has a capacity of 14.0 gallons, how many grams of gasoline are in your tank when it is fully? How many pounds?

Answer 1

The definition of density is: \(\sf \large density=\dfrac{mass}{volume}\)

You need to use that and a few conversion factors, gallons to \(m^3\), kg to grams, grams to pounds.

Answer 2

@aaronq I keep getting the wrong answers:

Density = mass
Volume Density = 732.22 kg/m3

Mass = ?

Volume = 14.0 gallons → m3

14.0 gal * 1 m3 = 0.0529957755 m3
264.172 gal

0.0529957755 m3 * 1000000 g = 52995.77548 g

Answer 3

It looks like you're using the right conversion for gallons, but I think your unit conversion for grams is off:

1 kg = 1,000 g

the prefix kilo- means a thousand, which is \(10^3\).

Answer 4

do i convert m^3 to kg? then kg to g?

Answer 5

Ahhh, no you can't convert \(m^3\) to \(kg\) because they're not different units for measuring the same thing. The first is volume, the second is mass. You can convert gallons to \(m^3\) because they're both different ways of measuring volume though.

So you only have to convert kg to g.

Answer 6

then how do you get kg?

Answer 7

I figured it out, thanks

Answer 8

Ahh, well you already had kg from your density, you are converting to g. Here, a small example (where I won't do any conversions)

Density\[\rho = 10 \frac{kg}{m^3}\]
Volume\[v= 3 m^3\]

So now we take our formula for density and rearrange by multiplying both sides by v \[\rho = \frac{m}{v} \implies \rho v = m\]

Then when we plug in our values for density and volume we get:

\[\rho v = 10 \frac{kg}{m^3} 3 m^3 = 30 \frac{kg}{m^3} m^3 = 30 kg\]

since \[\frac{m^3}{m^3}=1\] they divide out, since anything divided by itself is 1, even units just like \[\frac{7}{7}=1\]

So you can see the units ended up following through to the end leaving us with units of mass only, which is what we want, then we can multiply by our conversion factor \(\frac{1000 g}{1 kg}\) in this example to get the kg to divide out if we want our mass in grams.