What is the Concept of Volume?

  • Thread starter Thread starter batballbat
  • Start date Start date
  • Tags Tags
    Concept Volume
AI Thread Summary
The discussion centers on the concept of volume, particularly regarding a sphere with a hole and the implications of boundaries in geometric shapes. Participants clarify that a sphere and a ball are distinct, with the former referring to the surface and the latter to the solid. It is noted that a sphere with a hole theoretically retains the same volume as a solid sphere, as the hole's volume is negligible in mathematical terms. The conversation also touches on the difference between physical objects, like a cylinder with and without a lid, and idealized geometric shapes, emphasizing that only bounded solids have volume. Overall, the importance of precise terminology in discussing volume is highlighted.
batballbat
Messages
127
Reaction score
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
 
Mathematics news on Phys.org
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.
 
a cylinder without a lid has the same volume as a cylinder with lid. So it is not clear to me. Same for sphere
 
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.
 
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:
what is the volume of a sphere with a hole? so in geometry only bounded solids have volume, am i correct?
 
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.
 

Similar threads

B Volume of a Cube: Definition & Explanation
Replies
7
Views
5K
I Gabriel's Horn, Inside vs. Outside Surface area
Replies
9
Views
3K
I Volume of momentum space of an ideal gas
Replies
8
Views
2K
B Mass estimate only through mass rate of change
Replies
4
Views
1K
Doublet flow in Fluid Dynamics between two spheres or cylinders
Replies
0
Views
1K
B Calc Excess Rad on Earth in Curved 3D Space | Feynman Lectures 6-2
Replies
29
Views
2K
I Black Hole Diameter: Is It Finite or Infinite?
Replies
36
Views
6K
I Question about Integrals to Determine Volume vs Surface Area
Replies
5
Views
2K
A Interior volume of a black hole
Replies
23
Views
3K
General Query on Archimedes' Principle
Replies
14
Views
6K

Hot Threads

Recent Insights

Back
Top