Dave's ESL Cafe's Student Discussion Forums

[ShoHiro]

Hello teachers,

In an article I found the following terms "bulk form" and "volume." This article is how language structures space. According to this auther, you schematize(idealize) space to express the spatial terms. For example, a pencil is conceptualized(idealized) as a line--as when used with the preposition along.

"Bulk form" and "bulk" are used in the following context: where a bulk form with some concavity in it, such as a birdbath or a volcano, is conceptualized as a planar enclosure of volume.

"Bulk" in this sentence does not seem to mean "big," because a birdbath is not as big as a volcano. I have one more question in this sentence. What does the last phrase "a planar encloure of volume" mean? I don't understand what "volume" means here. I can't find an appropriate sense in the dictionaries. "Volume" here means approximately "three-dimensional solid"? If so, it contradict "a planer enclosure."

I'm sorry that it is very abstract question. I would like to know the meanings of "bulk" and "volume" in the sentence above in easier terms.

Best wishes
ShoHiro

[lotus]

Hi ShoHiro,

When something has bulk or is bulky, it occupies space (volume). Just as a pencil is long in one dimension, a volcano has bulk (volume) in three dimensions. The planar (two-dimensional) surface area of a volcano encloses the volume of the volcano.

A simple example would be a cube. The volume of a cube is x^3. The cube has six sides -- each of which has an area of x^2. So, the total surface area of a cube is 6x^2. This two-dimensional surface area encloses the cube.

In fact, to make a cube from a flat piece of paper, just draw six squares adjacent to each other in the pattern of a cross. Cut out the outer pattern and fold the edges where the squares meet. Tape all the edges together, and voila, you have a box.

A slightly more complex box:
http://www.tammyyee.com/origamiclover_box.html

Another example would be a sphere (ball). Its volume is 4/3(pi)(r^3). The surface area is 4(pi)(r^2). Although the object is a ball, the surface area which surrounds (encloses) the ball can be translated into a (flat) planar two-dimensional area whose value is 4(pi)(r^2).

http://www.gomath.com/algebra/sphere.php

The object does not have to be a cube or a ball. It can be any irregular three-dimensional shaped object. As long as it is enclosed, it has a surface area. This surface area of enclosure is the outer shape of the object.

The form (shape) of the bulk (volume) is the planar (area of) enclosure.

The bulk form is the volumetric shape of the object.



--lotus
_________________
War does not make one great --Yoda

[ShoHiro]

Hello lotus,

Thank you very much for answering in detail. I understand your explanation, 'the planar suface area of a volcano encolses the volume of the volcano.' I had the wrong idea about the phrase 'a planar enclosure of volume.' It does not contradicat "a planer enclosure."

'Bulk' means roughly volume, and 'volume' means roughly three-dimensional construction. Is this right?

I don't understand the represetations 'x^3,' 'x^2,' etc. It does not seem essential in the explanation, though. If you don't mind, could you tell me what they represent.

Sincerely,
ShoHiro

[lotus]

Hi ShoHiro,

1) Yes.

2) They represent "x cubed" and "x squared."

x cubed = x raised to the third power, or x times x times x.

x squared = x raised to the second power, or x times x.

"x^3" and "x^2" are standard notations when superscripts are not available. Notice that the upper arrow means "raised to the power of." That power is also called an exponent.


--lotus
_________________
War does not make one great --Yoda

[ShoHiro]

Hello lotus,

Thank you very much for a clear reply again!

I got it. "^" means "power." (I have not known that "power" has such meaning.)

Best wishes,
ShoHiro