An automobile gasoline tank holds 15.0 gal when full. How many pounds of gasoline will it hold if the gasoline has a density of 0.737 g/mL?
I would convert 15.0 gal to liters. There are 3.785 L in 1 gallon.Convert liters to mL. There are 1000 mL in 1 L.
Then mass in grams gasoline = volume in mL x density in grams/mL.
Now convert grams to pounds knowing there are 453.6 grams in 1 pound.
Post your work if you get stuck.
The density can be used as a conversion factor between mass and volume. Or, you can plug values into this formula and solve for the desired quantity.
density=massvolume
In the first calculation, you are given the mass in grams and the volume in cubic centimeters and asked to calculate the density in grams per cubic centimeter. Insert the given quantities into the density equation and solve for the density.
density=massvolume=50.3 g23.1 cm3=2.18 g/cm3
In the second calculation you are given the mass in grams and the density in grams per milliliter and asked to calculate the volume in milliliters. Rearrange the density equation to solve for the volume in terms of the density and mass.
volume=massdensity
Insert the given values and solve for the density.
volume=21.7 g0.791 g/mL=27.4 mL
Alternatively, you can use the density as a conversion factor to convert from mass to volume.
21.7 g×1 mL0.791 g=27.4 mL
In the third calculation, you are given the volume in gallons and the density in grams per milliliter and asked to calculate the mass in pounds. To be able to use the density as a conversion factor the volume must have the same units as the density. Start by converting the volume from gallons to milliliters.
17.0 gal×4 qt1 gal×1.00 L1.06 qt×1000 mL1 L=64200 mL
Then, either rearrange the density equation to solve for the mass in terms of the volume and density or use the density as a conversion factor to determine the mass in grams.
mass=density×volume
mass=0.737 g/mL×64200 mL=47300 g
or
64200 mL×0.737 g1 mL=47300 g
Finally, convert the mass from grams to pounds.
47300 g×1 lb454 g=104 lb
Well, if I did the math correctly and converted properly, a gallon of gasoline weighs about 6 pounds. So, if the tank holds 15 gallons when full, it will hold approximately 90 pounds of gasoline. That's like carrying around a very compact sumo wrestler! Just remember to fuel up responsibly and enjoy the ride!
To determine the weight of gasoline that the automobile tank will hold, we need to follow these steps:
Step 1: Convert the volume of the gasoline tank from gallons to milliliters.
The conversion factor is 1 gallon = 3.78541 liters = 3785.41 milliliters.
So, 15.0 gallons = 15.0 * 3785.41 mL = 56781.15 mL.
Step 2: Calculate the mass of the gasoline.
The density of the gasoline is given as 0.737 g/mL.
Mass = Volume × Density = 56781.15 mL × 0.737 g/mL = 41853.13955 grams.
Step 3: Convert the mass from grams to pounds.
The conversion factor is 1 pound = 453.59237 grams.
So, 41853.13955 grams = 41853.13955 / 453.59237 pounds = 92.25247 pounds.
Therefore, the automobile gasoline tank will hold approximately 92.25 pounds of gasoline.