What's the perimeter of a sphere?

Say the perimeter of a unit cube is 12, because that's the sum of all its edges, hence it's the cube's perimeter.

What would it be for a sphere of any proportion?

#MathProblem

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

We don't call the sum of the edge lengths of a polyhedron its "perimeter." A perimeter is the boundary of a two-dimensional figure.

Because a sphere has no edges, it has no such sum as you have defined with the cube. Your question is analogous to asking for the number of vertices of a circle. There is none.

hero p. - 8 years, 1 month ago

I interpret it as the sum of edges of a solid by your example of a cube. But a sphere has no edges, so the 'perimeter' is 0. If you are talking about adding all those tiny circumferences of the sphere up, you end up integrating them into the surface area of the sphere, $4\pi r^2$ .

Yong See Foo - 8 years, 1 month ago

Well you're just too smart for a 14 year old. I think that is kinda the answer.

Sanjay Ambadi - 8 years, 1 month ago

Correct.

Tim Ye - 8 years, 1 month ago

probably undefined since there are no edges on a sphere

Tan Li Xuan - 8 years, 1 month ago

i don't think it has a perimeter......as it is a 3D figure........

A Former Brilliant Member - 8 years, 1 month ago

bebzz.... see figure chaiye 3D ho yah 2D ....hum haar time perimeter find kaar sakte hai because vo humesha hi line segments se banni hoti hai .... and the figures with curves ,,hum unka circumfrence find kaar sakte hai ...."CIRCUMFRENCE" ......................remember hum circle ka circumfrence find karte thei......... same way sphere ka bhi circumfrence nikkal sakta hai.

Reshav Gupta - 8 years, 1 month ago

srry cant read hindi lol XD

Bob Yang - 8 years, 1 month ago

AND I would like to say one more thing.....next time dont...put ur silly...comments...in hindi.....

A Former Brilliant Member - 8 years, 1 month ago

@A Former Brilliant Member – It's same as that of a CIRCLE .......... 2pi R = circumfrence

Reshav Gupta - 8 years, 1 month ago

@Reshav Gupta – U are wrong,think of a sphere like a figure made of many circles of various sizes,the biggest being at the center,and decreasing gradually.what u said wouldn't make sense now would it?

Beakal Tiliksew - 8 years, 1 month ago

@Reshav Gupta – You cannot find the circumference of a sphere as such but you can find the circumference of the circles in it.

Aditya Parson - 8 years, 1 month ago

@Aditya Parson – decreasing...radii circles....will be there...

A Former Brilliant Member - 8 years, 1 month ago

@Reshav Gupta – ohhh i guess you aren't familiar...with sphere and its properties....it cant be 2pi R

A Former Brilliant Member - 8 years, 1 month ago

@A Former Brilliant Member – I DON'T THINK SO .......

Reshav Gupta - 8 years, 1 month ago

@Reshav Gupta – BUT I THINK SO.....AND BEFORE WRITING ANYTHING.....THINK OVER IT.......it will involve a typical integration with limits..... i think BK MAESTER T...is right.....

A Former Brilliant Member - 8 years, 1 month ago

ohk.....toh aap meko sphere ka " CIRCUMFERENCE " find karke do.....plzzzzz........woh bhi curve hai na........? :/

[ i said
fine! if is it so...then find "CIRCUMFERENCE" of...sphere since its a curve tooo....]
as u quoted "and the figures with curves ,,hum unka circumfrence find kaar sakte hai ...."CIRCUMFRENCE" same way sphere ka bhi circumfrence nikkal sakta hai. "

aur jab ho jae toh btana....me yahi milungi....except for the condition ki tum use kisise pucho ya fir koi search engine khol kar uspe se copy...paste karo.....huh....

[ i said when u'll finish that....post it here i'll be here only.....and terms and conditions for u.....DONT ASK IT FROM SOMEONE AND DONT CHEAT IT FROM SOME SEARCH ENGINE.....OK...]

A Former Brilliant Member - 8 years, 1 month ago

We define perimeter for 2-dimensional figures only.

Vikram Waradpande - 8 years, 1 month ago

There is no perimeter in 3 dimensional.Please clarify your question

EDSEL SALARIOSA - 8 years, 1 month ago

Tim Y. has already defined a "perimeter" of a 3D solid to be the sum of its edges. It is on our part, and not his, to understand what is implied.

Wee Xian Bin - 8 years, 1 month ago

Perimeter doesn't apply to 3 dimensional figures. It is the boundary of a 2 dimensional figure.Since, 3 dimensional figures don't have any boundary , so, neither a sphere nor a cube has a perimeter.

Prakkash Manohar - 8 years, 1 month ago

Well, going by your definition, lets say the sphere has infinite sides, then Perimeter = (infinity) x (whatever is the value of each side) p = ∞ But wait, the length of each side is zero as they are just points. ∴ p = ∞ x 0 = 1 (if you can consider that as true) Hence your answer is 1.

Sanjay Ambadi - 8 years, 1 month ago

Guyss.... first of all , cube is also a 3D figure and In the figures like that of a circle or a sphere ,we don't take perimeter ,there it's circumfrence . And in sphere we can have the circumfrence .. agree?

Reshav Gupta - 8 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$