on a three dimensional figure surface area is the area of the space on the very outside of the figure
nothing on the inside
2007-03-18 16:17:21
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answer #1
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answered by tyder21 4
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Yes, the surface area of something is the area of the SURFACE that completely ENCLOSES that something! It's generally the term applied to finding the full TWO-DIMENSIONAL AREA of the "bounding surface" of a THREE-DIMENSIONAL BODY (such as a cube, tetrahedron, American football, sphere ... .)
For example, suppose that you have a solid spherical ball, that looks absolutely identical from ANY direction:
Its "Cross-sectional area" (the area of a circle produced by any plane passing through its centre) is simply the FLAT, PLANE area enclosed by the circle that that process produces in space. (You wouldn't normally call THAT area a "surface area," since the AREA itself doesn't ENCLOSE anything completely. That's a terminological problem with a responder talking about the "surface area"of a table top. That is more properly exactly THIS : the AREA of the table top, not the "surface area of the table."
Getting back to the area of the plane cross-section of the sphere, that area is
Ï r^2,
where ' r ' is the RADIUS of the SPHERE.
However, the SURFACE AREA of that sphere is the area of the complete SPHERICAL SURFACE that separates the INTERIOR of the sphere from the outside world. Although it's NOT FLAT, that area can in fact be worked out by imagining dividing it into lots of little, adjacent areas that ARE flat, to all intents and purposes. (The idea is to divide it into smaller amd smaller pieces and see what limit the sum of all these tiny areas approaches as they become individually smaller and smaller.)
The great Greek mathematician (and physicist) Archimedes did this very derivation, OVER TWO THOUSAND YEARS AGO (!), and he found that the complete surface area of a sphere was:
4 Ï r^2.
In other words, the SURFACE AREA of a SPHERE is precisely FOUR times the area of any of its flat "equatorial cross-sections."
This was an incredibly important result, having implications is many diverse field from mathematics to physics, astronomy and astrophysics.
I hope that this example of a non-trivial (not flat) surface- (or "bounding-") area has given you some idea of what the concept means, in general.
Live long and prosper.
2007-03-18 23:28:22
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answer #2
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answered by Dr Spock 6
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surface area is the area of all surfaces of a three dimensional object. like, for a cube with sides with a length of 5, you would do 5 times 5 for one side of it, which is 25, then you multiply that by the number of sides a square has, which is 6, and get 150 units squared.
2007-03-18 23:27:04
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answer #3
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answered by h.pfanatic 2
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It is the total area of all the surfaces on a particuler object...
eg a cube of 5cm sides..
has 6 faces ... the faces have a surface of 25 sq cm
so total surface area is 6 X 25 = 150 sq cm...
2007-03-18 23:18:38
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answer #4
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answered by Anonymous
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it is the area of the surface of a three-dimensional object. take for example, a ball in the shape of a sphere. the surface area is how big the outside is.
2007-03-18 23:16:49
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answer #5
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answered by metalluka 3
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Example: Take a table and measure its length and width.
Multiply the two figures together and you'll have the surface area of the table in units squared. (The length and width must be in the same units before multiplying them)
Example: a table has a length of 5 feet (or metres) and a width of 2.5 feet (or metres)
Surface area = 5 x 2.5 = 12.5 square feet (or square metres).
(12.5ft²) or (12.5m²)
2007-03-18 23:20:54
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answer #6
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answered by Norrie 7
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