- #1

- 52

- 0

If I integrate that I get 1/3 (pi)r^3, which is close to the volume of a sphere. But where do I get a 4/3(pi)r^3 ?

- Thread starter Silverious
- Start date

- #1

- 52

- 0

If I integrate that I get 1/3 (pi)r^3, which is close to the volume of a sphere. But where do I get a 4/3(pi)r^3 ?

- #2

arildno

Science Advisor

Homework Helper

Gold Member

Dearly Missed

- 9,970

- 132

Differentiate the volume expression, and find a suitable interpretation of the result.

Last edited:

- #3

matt grime

Science Advisor

Homework Helper

- 9,395

- 3

beacause disks are not the infinitesimal shells that add up to a solid sphere

- #4

- 52

- 0

I would find out for myself but I'm a little busy.

Thanks for the replies.

- #5

matt grime

Science Advisor

Homework Helper

- 9,395

- 3

that's a different technique: add up the shells of surface area of a sphere

- #6

- 52

- 0

OKay I'm starting to understand.

So I use the surface area formula(for a sphere). Integrate from 0 to r? :uhh:

Edit: Oh my god. I feel so stupid...

You see, I didn't know the formula for the surface area of a sphere. ......

Oh well. Anyways, uum. So then, what is 1/3(pi)r^3? Without looking it up, making a wild guess...is it the volume of a cylinder?

Edit2: I really need to stop thinking.... I have no clue what I'm talking about. :yuck: So is 1/3(pi)r^3 just nonsense?

Edit3: Interesting that a cone's volume is 1/3(pi)r^2 h. Good I have much time to think about it.

So I use the surface area formula(for a sphere). Integrate from 0 to r? :uhh:

Edit: Oh my god. I feel so stupid...

You see, I didn't know the formula for the surface area of a sphere. ......

Oh well. Anyways, uum. So then, what is 1/3(pi)r^3? Without looking it up, making a wild guess...is it the volume of a cylinder?

Edit2: I really need to stop thinking.... I have no clue what I'm talking about. :yuck: So is 1/3(pi)r^3 just nonsense?

Edit3: Interesting that a cone's volume is 1/3(pi)r^2 h. Good I have much time to think about it.

Last edited:

- #7

matt grime

Science Advisor

Homework Helper

- 9,395

- 3

the surface area of a sphere is 4(pi)r^2

- Last Post

- Replies
- 5

- Views
- 6K

- Replies
- 7

- Views
- 2K

- Replies
- 2

- Views
- 1K

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 1K

- Last Post

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 3K

- Last Post

- Replies
- 5

- Views
- 2K

- Last Post

- Replies
- 12

- Views
- 2K