Math Problem of the Week

Submitted by david.thacker on
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Snow Water Equivalence Problem

      Winter weather can result in snowstorms dumping large amounts of snow in a short time. The Snow Water Equivalent (SWE) is a common snow pack measurement to tell the amount of water contained within the snow pack. It is the depth of water that would result if the entire snow pack melted.

       For example, if an empty wading pool filled with 20 inches of new powdery snow at 0.15 snow water density and the snow is melted, you would be left with a pool of water 3 inches deep. In this case, the SWE of your snow pack would equal 20 × 0.15 = 3 inches.

       To determine snow depth from SWE you need to know the density of the snow. The density of new snow ranges from about 0.05 when the air temperature is 14° F, to about 0.20 when the air temperature is 32° F. After the snow falls its density increases due to gravitational settling, wind packing, melting and recrystallization.

The relationship between the snow water equivalent, snow density and snow depth is modeled with the following formula: 

snow water equivalent ÷ snow density = snow depth 

     Snow from a recent snowstorm filled an empty cylindrical trash can 28 inches tall. When the snow was melted, the height of the water in the trash can was 17 cm. What was the density of the snow? Express your answer as a decimal to the nearest hundredth. Be sure to show your work or explain how you got your answer.

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