Understanding Surface Area: Foldings, Invaginations, Roughness & Powder

[gracy]

why surface area increases with foldings ,invaginations,roughness and powdered form?please someone explain concept of surface area.

what is difference between perimeter or (circumference in case of circle)and surface area?

Mentor Note: Two posts have been merged.

 

[Nugatory]

The term "perimeter" is usually reserved for the length of the boundary of a two-dimensional shape, while "surface area" applies to the boundary of a three-dimensional volume.

 

[td21]

perimeter has units of length while surface area has units of length squared.

 

[gracy]

The term "perimeter" is usually reserved for the length of the boundary of a two-dimensional shape, while "surface area" applies to the boundary of a three-dimensional volume.

sir why boundary of a two-dimensional shape can be expressed in length but boundary of a three-dimensional object i.e surface area require length squared?

 

[UncertaintyAjay]

I reckon its the nature of the space you're talking about. In 2 dimensions, shapes are bounded by lines and curves. So , there you can about these boundaries in terms of perimeter. In 3 dimensions, objects are bkubded by surfaces( e.g, a cube is bounded by 6 surfaces, a sphere by 1) so its more meaningful to talk about the area( length squared dimensionally) than it is to talk about the length of a surface.

 

[gracy]

I reckon its the nature of the space you're talking about. In 2 dimensions, shapes are bounded by lines and curves. So , there you can about these boundaries in terms of perimeter. In 3 dimensions, objects are bkubded by surfaces( e.g, a cube is bounded by 6 surfaces, a sphere by 1) so its more meaningful to talk about the area( length squared dimensionally) than it is to talk about the length of a surface.

how you came to know that sphere is bounded by 1 surface,?which surface is this?

 

[UncertaintyAjay]

Well think about it.
A cube has 6 sides- six plane surfaces that bound it. Take something spherical, run your hand over it and see if you ever come to an edge. That's why there is no "worlds end" .you sail as far as you want, and you'll never fall over the edge of the Earth because there isn't one. It's one continuous surface.

 

[UncertaintyAjay]

Well think about it. A sphere doesn't have any edges its continuous.
Look at the earth. You can't sail over the edge of the world because there isn't one. You can sail on and on forever and never fall off or encounter an edge because it all one continuous surface.

 

[gracy]

Well think about it. A sphere doesn't have any edges its continuous.
Look at the earth. You can't sail over the edge of the world because there isn't one. You can sail on and on forever and never fall off or encounter an edge because it all one continuous surface.

good one!

 

[UncertaintyAjay]

Thanks

 

[gracy]

while "surface area" applies to the boundary of a three-dimensional volume.

length of the boundary?

 

[Nugatory]

length of the boundary?

OK, so the English language isn't perfect... It's not my fault that English uses different words for the N=2 and N=3 cases of the N-1-dimensional boundary of an N-dimensional space.

You could say "intuitive quantitative measure of the boundary of a region", and reserve the word "length" for the special case of the one-dimensional boundary of a two-dimensional surface.