Converting 3-dimensional space
By this point you should be able to
- convert anything to anything else easily, using a chain of fractions that equal 1
- follow the units to ensure that you are doing the conversions correctly
- know how to adjust for the same unit appearing twice (or more)
In biology, we often see a situation where we need to take 3-dimensional habitat into consideration. For example, rats can live on all levels of a parking garage, and they use the spaces between floor and ceiling as well, so it may be more accurate to measure their density per cubic meter, rather than per square meter.
The parking garage at Mall of America is 0.8 km long, 0.3 km wide, and 0.1km high. If there are a total of 20,000 rats in the parking garage, then what is the density per cubic meter?
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- Volume of garage in km^3: 0.8km x 0.3km x 0.1km = 0.024km^3
- How many conversions?: 3 dimensions = 3 conversions from km to m
- Total volume of garage in m^3 : 0.024 km^3x 1000m/1km x 1000m/1km x 1000m/1km = 2.4 million m^3
- rat density : 20,000 rats / 2.4 million m^3
I think I have the answer: 0.008 rats / m^3
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