2011-06-29, 05:39 AM
(This post was last modified: 2011-06-29, 07:07 AM by 2147483647.)
Length is a measure of distance. Volume is a measure of how much space an object occupies. Length is a one-dimensional measurement, and volume is a three-dimensional measurement. We live in a three-dimensional world, and it's only natural that real objects take up three-dimensional space. If an object only takes up one dimension, then it's obviously massless, and the only thing that is massless is light, which also isn't a tangible object.
That being said, let us consider two objects. Object one is a cylindrical object of radius 2 and length 3. Object two is a cylindrical object of radius 1 and length 4. If these objects both have the same mass density, it's pretty obvious that object one is superior to object two in mass. Object one has a mass of 12π, while object two only has a mass of 4π. Object one occupies three times the space of object two, even though object two is longer by a single unit.
By the way, some shapes are also superior. For example, spheres are superior to cones. But I will let you justify that.
That being said, let us consider two objects. Object one is a cylindrical object of radius 2 and length 3. Object two is a cylindrical object of radius 1 and length 4. If these objects both have the same mass density, it's pretty obvious that object one is superior to object two in mass. Object one has a mass of 12π, while object two only has a mass of 4π. Object one occupies three times the space of object two, even though object two is longer by a single unit.
By the way, some shapes are also superior. For example, spheres are superior to cones. But I will let you justify that.