Math CentralQuandaries & Queries


Question from Kevin:

I have a 20,000 gallon fuel bag Length 32'x Width 29'x Height 4.2'. I need to build a containment around it. If the bag was to rupture the containment would have to hold the 20,000 gallons of fuel plus ten percent. What size would the containment have to be in order to hold the fuel..

Hi Kevin. If you want the proportions of the containment to match that of the bag, then you could calculate it this way:

I want the volume to increase by 10%, that means it is multiplied by 1.10.

I want the length, width and height to increase at equal proportions.

So 1.10 = p3, so p = 1.0323.

Thus all dimensions should be multiplied by 1.0323.

That makes 33.03' x 29.94' x 4.34'.

Let's check this:
32' x 29' x 4.2' = 3897.6 cubic feet for the fuel bag.
33.03' x 29.94' x 4.34' = 4291.9 cubic feet for the containment.
4291.9 / 3897.6 = 1.101 = 10.1% extra volume (this is due to rounding).

Hope this helps,
Stephen La Rocque.

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