Question

Based on the imperial unit system, currently in use only in Liberia, Myanmar, and the United States, engineers use the acre-foot, as a volume unit. It is defined as 1 acre of land to a depth of 1 ft. Last spring, a severe thunderstorm dumped 2.5 in. of rain in 30 min on the town of Avon, which has an area of 101 km2. What volume of water, in acre-feet, fell on the town?

Answer 1

In this type of problems what we have to do is unit conversion. In order to do so we need all the equivalences which we will be mentioning during the explanation of the problem:

First of all the answer is asked to be in acre-feet and we can see the data we are getting from the rain is in $in*Km^{2}$ not even a volume unit.

To calculate the volume of poured rain we need to have both numbers in the same units, we will convert $Km^{2}$ to $in^{2}$ using the equivalence $1 Km^{2}=1550001600in^{2}$ like this:

$101Km^{2}*\frac{1550001600in^{2} }{1Km^{2}}=156550161600in^{2}$

it is possible now to calculate the volume ($Volume_{cuboid}=Area*Height$) like this:

$Volume_{cuboid}=156550161600in^{2}*2.5in=391375404000in^{3}$

Now we just need to convert this volume to acre-feet and we will do so using the equivalence $1acre-foot=751271680in^{3}$ like this:

$391375404000in^{3}*\frac{1acre-foot}{751271680in^{3}}=5199.50403658 acre-feet$

5199.50403658 acre-feet would be the answer to our problem