Oil spill including volume,area but unknown thickness

Question

If I know total gallons of oil spilled is 94,000 gallons and area is 5 miles by 2 miles long how do I find total thickness in millimeters

Answer 1

If you assume that the spill can be treated like a rectangular prism, then the total volume of oil is equal to the surface area of the spill multiplied by its thickness - i.e. $V = SA \times h$. The only problem is that you're given volume in gallons and area in square miles, but you're meant to find the thickness in millimetres. So you need to do some unit conversions, which can be summarised as follows:

$h \mbox{ mm} = \frac{V \mbox{ gal}}{SA \mbox{ mi}^2} \times \frac{3 785 411 \mbox{ mm}^3}{1 \mbox{ gal}} \times \left ( \frac{1 \mbox{ mi}}{1 609 344 \mbox{ mm}} \right )^2$

although there's a decent chance that you have a recommended method for converting between some of these values from your textbook or teacher.

Once you've figured that out, you can check your answer by typing (without quotes): "94000 gallons / 10 square miles in mm" into Google.

Answer 2

Hint: $1$ gallon is $231$ cubic inches. $1$ mile is $63360$ inches. $1$ inch is $25.4$ millimeters.

The spill is $94000\times231$ cubic inches in volume and $5\times63360\times2\times63360$ square inches in area.