Why is the volume of a rectangular object measured in cubic units?

length x width x height = xunits鲁





eg. What is the volume of a box of length 3m, width 4m and height 2m?


3mx4mx2m= 24m鲁Why is the volume of a rectangular object measured in cubic units?
A rectangle is 2 dimensional so it is not measured in cubic units. A 3 dimensional object that has all faces either rectangular or square is measured in cubic units because they fit. Trying to measure or calculate the volume of a cube in spherical units would make no sense at all.Why is the volume of a rectangular object measured in cubic units?
If you want to specify the length of an object, imagine summing up the length of lots of very short lines along the side of the object you are interested in.





If you want to specify the area of a rectangular object, imagine summing up the lengths for each line across the rectangle.





If you want to specify the volume of a box object, imagine summing up the areas for each filled rectangle across the box.





So, using a cartesian coordinate system:








l=危dx


A=h鈭櫸


V=d鈭櫸





Now let's say you have measured the length in meters:


l=5m


then you also found out ';how many'; of the lengths are in an area by measuring the length in the other direction (that is, ';h';).


so let's say h=3m.


Then you also found out ';how many'; of the filled rectangles are in a box by measuring the length in the remaining direction (that is, ';d';).


so let's say d=2m.





So now the total volume V is:


V=5m鈭?m鈭?m=30m鲁.