DAT math...wat does this mean?

[illbirz]

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The intuition here is that proportional enlargement of three-dimensional objects increases their volume as the cube of their linear (one-dimensional) dimensions. 😕

 

[jntruong2003]

haha, it seems like a ******ed and obvious analysis. the way i look at it is that is that it is saying that when the length of a side increases of a 3 dimensional object= increased volume as well as the increase of a side of a planar object= increased area. but that's how i understood it.

 

[Scott Kane]

All it's saying is that for every unit (x) that the dimension of an object increases, then its volume will be increased by x^3. For example, say a you have a cube whose sides are equal to x and volume is x^3. If you increase the size of the cube's side to say (x+1), then the volume will increase (x+1)^3. Same for a sphere if V = 4/3pi*r^3. If you increase r to (r+1), then the volume increases by (r+1)^3.

 

[Streetwolf]

If the length of a side of a cube is increased 3-fold then the volume is increased 27-fold (3^3). Just an example.