A square measuring 5" × 5" has a surface area of 50 in²
Doesnt each square have a front side and a reverse side?
If I asked to measure the surface area of a cube, arent all sides considered?
Imagine a hollow, open-ended cylinder. The surface area would be both internal and external... plus the areas of the ends - the donut shapes, connecting internal and external... not the hollow center. Why is it this is a consistent rule for cylinders of this design... but when we take the limit of the surface area as the the width of the donut gets smaller, the area is relatively constant. But when the width reaches zero, the ares is suddenly cut in half for only arbitrary reasons - that being the cylinder is now a two dimensional object curving in on itself in three dimensional space
2007-11-20 18:04:29 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
squared is only two dimensions.
a square only has a front side and a back side when it is considered three dimensional, and at that point, the area is still 25 inches squared, but the surface area is twice that, if one assumes the edges have negligible area.
also, as the hole in the cylinder gets smaller, the surface area stays the roughly the same to account for the width at the top and the bottom of the cylinder getting thicker.
think of surface area as the spaces where air can touch, but 'area' as the amount of space that something takes up.
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people, he never asked the surface area of a cube - reread the question.
2007-11-20 18:11:33 · answer #1 · answered by Jim 7 · 0⤊ 0⤋
First, a square can't have surface area because surface area applies to three-dimensional figures and a square is two-dimensional. You can't think of 2D objects as infinitely curved at the edge in a 3D world. 2D is just an idea, and 3D is reality as we see it. But if you use this idea that 2D is just a shape with edges infinitely tightly curved in 3D space, then yes, I suppose theoretically the surface area is 50in²...
A cube and a square are different. A square as I said before is just an idea, a representation of a surface of a cube, but we assume that a cube is reality. So you can't say a square is actually just a really thin cube.
For the cylinder, it is in reality impossible, but even theoretically, the transformation from a 3D object to a 2D object is a very good reason to halve the surface area, not that you can apply the term "surface area" to a truly 2D shape. But my key point in this is that 2D is not just 3D with an one infinitely small dimension, but a whole different idea....
2007-11-21 02:24:25 · answer #2 · answered by Anonymous · 0⤊ 0⤋
5" * 5" = 25 in²
Surface area is considered to be a two dimensions structure. It's considered to be so tin that it doesn't have a thickness. So to measure it on the front and on the back would be the same measurement taken twice.
A cylinder with zero thickness will be in two dimensions and so will no longer be a three dimensional cylinder.
2007-11-21 02:23:16 · answer #3 · answered by Sparks 6 · 0⤊ 0⤋
The area of a 5" x 5" square is 25 square inches, not 50!
And I'm not sure what you mean by "a front side and a back side".
If you are measuring surface area of a cub you have to consider all sides.
And I'm not sure about your last question either. Sorry!
2007-11-21 02:15:45 · answer #4 · answered by smarties 6 · 0⤊ 2⤋
A square represents a plane, 2D. There is no reverse side to a plane. There may be inner and outer surfaces to a cylinder, but that's a 3D object. Apples and oranges.
2007-11-21 02:32:26 · answer #5 · answered by Dinky 3 · 0⤊ 0⤋
It would be 150 square in. It is 25 square in. on each side. there are 6 sides.
2007-11-21 02:07:50 · answer #6 · answered by Alana B 1 · 0⤊ 2⤋
5x5 does = 25... but there are 6 sides to a square... so you would have to times 25x6 ... which would = 150!
2007-11-21 02:12:12 · answer #7 · answered by foxracerhb2006 2 · 0⤊ 2⤋