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 Question from Fred, a parent: HOW MUCH WATER IS THERE IN A CUBIC MILE?

Hi Fred. To convert this to something more familiar, you can first convert it to cubic feet:

1 mile = 5280 ft, so (1 mile)3 = (5280 ft3) = 52803 ft3 = 147197952000 ft3.

Now we can convert that to some more familiar volume measures.

Each foot is 3.048 decimeters (dm) and since 1 dm3 is a litre, we have:

147197952000 ft3 = 147197952000 (3.048 dm)3 = 147197952000 x (3.0483) litres = 4168181825441 litres.

If you prefer US gallons, you need to look up the conversion: 1 ft3 = 7.48051948 US gallons, so

147197952000 ft3 = 147197952000 (7.48051948 US gallons) = 1101117147352 US gallons.

Big numbers like these are rather hard to picture. That's about as much water as flows over Niagara Falls in about a month.

Another comparison: The land area of Manhattan Island in New York City is 22.96 square miles. So if we divide 1 cubic mile by 22.96 square miles, we have 1/22.96 miles = 230 ft. So if you built a retaining wall
around Manhattan and poured 1 cubic mile of water into it, only buildings taller than 23 stories would break the surface!

Cheers,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.