Math CentralQuandaries & Queries


Question from Michael:

I have a storage tank that is 12' diameter x 22.5' high
it's capacity is 450 oil field barrels (42 gallon)
Which would hold 19,036 us gallons
I'm trying to find out how many inches it would take to make 1 barrel
I was able to get this far by using your volume calculator, but haven't been able to come up with the rest!
Thank you very much for your time, and I really appreciate this site and the tools you all have made available to everyone for free!
Hope to hear back from you soon and God bless you all!!

Hi Michael,

Thank you for the kind words.

Our volume calculator gives a volume of 19,036 US gallons for your tank as you said but 450 oil field barrels at 45 US gallons per barrel gives $450 \times 42 = 18,900$ gallons. I think the storage tank manufactures don't think the tanks will be completely full.

If you use our volume calculator for a cylinder with diameter 12 feet and depth 1 inch you get a volume of 70.5 US gallons. Thus to get 42 gallons, one oilfield barrel you need about $\frac{42}{70} = 0.6$ inches.

Lets do it more exactly. The volume of a cylinder is

\[\pi \; r^2 h \mbox{ cubic inches}\]

where $r$ is the radius in inches and $h$ is the height in inches. There are 231 cubic inches in a US gallon so if the volume is to be 42 US gallons then

\[42 \times 231 = \pi \; (6 \times 12)^2 h.\]

Solving for $h$ gives

\[h = \frac{42 \times 231}{\pi \; \times (6 \times 12)^2} = 0.596 \mbox{ inches.}\]

I hope this helps,

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