Math CentralQuandaries & Queries


Question from Hannan, a student:

Lake Utah has a surface area of 3,846 square miles and an average depth of 10.5 feet. In cubic miles, how much water does it hold?
How would you approach this question? Where would you start?
I tried to do a conversion: I did 1 mile=5280 ft then I multiplied 43 ft. But how do I get cubic mile?

Hi Hannan,

The volume in cubic units is the surface area times the average depth and you have the surface area in square miles so you need the depth in miles. Use the fact that 1 miles is 5280 feet to convert the depth to miles and then calculate the volume in cubic miles.

Write back if you need more assistance,


The easiest way to do this it to convert the depth into miles: (10.5/5280) miles. Then multiply by the surface area (already in square miles) to get cubic miles.) The answer to the division is so close to a round decimal (check this!) that I suspect it was picked for that purpose.

Some people will convert square miles into square feet (x 5280^2), multiply by 10.5, then convert back from cubic feet to cubic miles. This is less efficient, but many people are not used to using miles to express small distances.

If this was not a class assignment, so you did not need to show your work, you could Google

[3846 * 10.5 feet in miles ]

and get the right answer. Note that the "feet in miles" must come last.

Good Hunting!

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