What is the Concept of Volume?

In summary, the concept of volume can be confusing, especially when dealing with unusual terminology and abstract concepts. In geometry, only bounded solids have a defined volume, and the volume of a sphere with a hole is the same as a solid sphere without a hole. When discussing volume, it is important to be precise and use clear definitions.
  • #1
batballbat
127
0
i am having confusion with the concept of volume. Does a sphere with a hole have the same volume as the volume of a sphere? I think it doesent, but if the hole is sufficiently small, they would hold the same amount of fluid. Also the hollow space of sphere counts as its volume. Then why doesent a curved plane which covers some hollow space count as its volume. please give me a detailed definition of volume
 
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  • #2
I'm not entirely sure what you're talking about here. What do you mean by "why doesent a curved plane which covers some hollow space count as its volume?"

Part of the problem seems to be that you're using strange terminology. Generally, the term "sphere" refers refers to the surface of a ball, but you seem to be using "sphere" and "ball" interchangeably, and so I have no idea what a "hole in a sphere" is supposed to be. The notion of volume is an intuitive concept; if you want a "detailed" rigorous explanation, you need real analysis.
 
  • #3
a cylinder without a lid has the same volume as a cylinder with lid. So it is not clear to me. Same for sphere
 
  • #4
batballbat said:
a cylinder without a lid has the same volume as a cylinder with lid. So it is not clear to me. Same for sphere

And you just said it. A sphere with a "hole" has the same volume as one that doesn't.
 
  • #5
batballbat said:
a cylinder without a lid has the same volume as a cylinder with lid. So it is not clear to me. Same for sphere
A cylindrical can, for example, does NOT have the same volume with and without the lid because these are actual physical things and both can and lid have volume.

But the mathematical, ideal, solid has boundary with 0 thickness. The "top" of such a cylinder has 0 volume.
 
Last edited by a moderator:
  • #6
what is the volume of a sphere with a hole? so in geometry only bounded solids have volume, am i correct?
 
  • #7
batballbat said:
what is the volume of a sphere with a hole? so in geometry only bounded solids have volume, am i correct?

I think you need to be more precise in your descriptions. The region of 3 space defined by:

x2 + y2 + z2 < r2

has the same volume as

x2 + y2 + z2 ≤ r2

even though the first doesn't include the boundary, while the second does.
 

1. What is volume?

Volume is a measurement of the amount of space occupied by an object or substance. It is often measured in units such as liters, cubic inches, or cubic meters.

2. How is volume different from mass?

Volume and mass are two different measurements. Volume measures the amount of space taken up by an object, while mass measures the amount of matter in an object. Volume can change depending on the shape and size of an object, while mass remains the same.

3. What is the formula for calculating volume?

The formula for calculating volume varies depending on the shape of the object. For a rectangular object, the formula is length x width x height. For a cylinder, the formula is π x radius² x height. Other shapes have their own specific formulas for calculating volume.

4. How is volume used in everyday life?

Volume is used in many everyday situations, such as measuring liquids for cooking or baking, determining the amount of water needed for a swimming pool, or finding the right size container for storage. It is also an important concept in industries such as construction, engineering, and manufacturing.

5. How does volume relate to density?

Density is a measure of how much mass is contained in a certain volume. The formula for density is mass divided by volume. This means that volume plays a crucial role in determining the density of a substance or object.

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