#$&*
course PHY 241
08/30/2011 245pm
`aThere are 1000 cm^3 in a liter and 1000 liters in a m^3, so there are 1000 * 1000 = 1,000,000 cm^3 in a m^3.
It's important to understand the 'chain' of units in the previous problem, from cm^3 to liters to m^3. However another way to get the desired result is also important:
There are 100 cm in a meter, so 1 m^3 = (1 m)^3 = (100 cm)^3 = 1,000,000 cm^3.
STUDENT COMMENT
It took me a while to decipher this one out, but I finally connected the liters to cm^3 and m^3. I should have calculated it by just converting units, it would have been easier.
INSTRUCTOR RESPONSE
The point isn't just conversion. There are two points to understanding the picture. One is economy of memory: it's easier to remember the picture than the conversion factors, which can easily be confused. The other is conceptual/visual: the picture gives you a deeper understanding of the units.
In the long run it's easier to remember that a liter is a 10-cm cube, and a cubic meter is a 100-cm cube.
Once you get this image in your mind, it's obvious how 10 layers of 10 rows of 10 one-cm cubes forms a liter, and 10 layers of 10 rows of 10 one-liter cubes forms a cubic meter.
Once you understand this, rather than having a meaningless conversion number you have a picture that not only gives you the conversion, but can be used to visualize the meanings of the units and how they are applied to a variety of problems and situations.
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Self-critique (if necessary):"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#$&*
course PHY 241
08/30/2011 245pm
`aThere are 1000 cm^3 in a liter and 1000 liters in a m^3, so there are 1000 * 1000 = 1,000,000 cm^3 in a m^3.
It's important to understand the 'chain' of units in the previous problem, from cm^3 to liters to m^3. However another way to get the desired result is also important:
There are 100 cm in a meter, so 1 m^3 = (1 m)^3 = (100 cm)^3 = 1,000,000 cm^3.
STUDENT COMMENT
It took me a while to decipher this one out, but I finally connected the liters to cm^3 and m^3. I should have calculated it by just converting units, it would have been easier.
INSTRUCTOR RESPONSE
The point isn't just conversion. There are two points to understanding the picture. One is economy of memory: it's easier to remember the picture than the conversion factors, which can easily be confused. The other is conceptual/visual: the picture gives you a deeper understanding of the units.
In the long run it's easier to remember that a liter is a 10-cm cube, and a cubic meter is a 100-cm cube.
Once you get this image in your mind, it's obvious how 10 layers of 10 rows of 10 one-cm cubes forms a liter, and 10 layers of 10 rows of 10 one-liter cubes forms a cubic meter.
Once you understand this, rather than having a meaningless conversion number you have a picture that not only gives you the conversion, but can be used to visualize the meanings of the units and how they are applied to a variety of problems and situations.
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!