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Subject: "Circumference of a sphere"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #279
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Ariyan
Member since Feb-22-04
 Mar-22-04, 07:19 PM (EST)
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"Circumference of a sphere"
 
   Hello,

I don't know if this is a frequently asked question, but is there a way to calculate the circumference of a sphere with radius r? I think there isn't. But if there is a way, I would appreciate it if nobody told me how. But if there is a way, I would like it if anybody could tell me why.

Thank you,
Ariyan from the Netherlands


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  Subject     Author     Message Date     ID  
Circumference of a sphere Ariyan Mar-22-04 TOP
  RE: Circumference of a sphere alexb Mar-22-04 1
     RE: Circumference of a sphere Ariyan Apr-15-04 5
  RE: Circumference of a sphere TJ Mar-29-04 2
     RE: Circumference of a sphere Graham C Mar-30-04 3
         RE: Circumference of a sphere Ariyan Mar-30-04 4
  RE: Circumference of a sphere Leah Nov-03-04 6
     RE: Circumference of a sphere Guest Mar-17-06 7

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alexb
Charter Member
1800 posts		 Mar-22-04, 07:20 PM (EST)
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1. "RE: Circumference of a sphere"
In response to message #0
 
   >I don't know if this is a frequently asked question, but is
>there a way to calculate the circumference of a sphere with
>radius r?

What is the circumference of a sphere? How do you define it?


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Ariyan
guest
 Apr-15-04, 12:22 PM (EST)
 
5. "RE: Circumference of a sphere"
In response to message #1
 
  

Your answer:

Sphere Surface Area = 4 · p · r 2

Regards,
Gene



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TJ
guest
 Mar-29-04, 07:11 PM (EST)
 
2. "RE: Circumference of a sphere"
In response to message #0
 
   Perhaps you mean the surface area of a sphere? THAT particular quantity is indeed calculatable by a rather simple mathematical formula. If you mean the circumfrence of the golden circle of a sphere (that is, a circle which shares the same center as the sphere itself but occupies only one flat plane, whose edge traces the edge of the sphere), that is simply 2(pi)(r) where r is the radius.


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Graham C
Member since Feb-5-03
 Mar-30-04, 07:49 AM (EST)
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3. "RE: Circumference of a sphere"
In response to message #2
 
   Slightly more complicated would be the circumference of a circle drawn on the surface of the sphere - i.e. the circle is the locus of the points on the sphere's surface equidistant from a given point.

Let the radius of the sphere be R, and the radius of the circle (measured on the surface of the sphere: an arc) be D. Then the angle A subtended at the centre by the arc is D/R rads, and the radius of the circle in the plane that it defines is R*sin(A), so its circumference is 2*pi*R*sin(A) or
2*pi*R*sin(D/R).


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Ariyan
Member since Feb-22-04
 Mar-30-04, 11:32 PM (EST)
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4. "RE: Circumference of a sphere"
In response to message #3
 
   Dear TJ and Graham C,
I was thinking about the questions that Dr Alex B posted and realised I couldn't answer them since I was searching for the circumference but looking at the area of the sphere. I was a little bit confused I guess. But after your posts I found out again why I was confused.
If you can calculate all the circumferences of the circles drawn on the surface of a sphere you would have the circumference of a sphere, I thought.

Thanks
Ariyan


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Leah
guest
 Nov-03-04, 08:51 PM (EST)
 
6. "RE: Circumference of a sphere"
In response to message #0
 
   The formula for the circumference of a sphere is just the derivative of the volume formula...

V = (4/3)pi r^3
V' = 4 pi r^2 = circumference


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Guest
guest
 Mar-17-06, 02:32 PM (EST)
 
7. "RE: Circumference of a sphere"
In response to message #6
 
   Nope - thats the area.

Circumference is a 2 dimensional measurement; therefore, the circumference of a sphere is 2*pi*r, same as a circle.

This coincides with the popular calculus question regarding derivitives: "The circumference of a sphere was measured at 84cm with a 0.5cm margin of error. Estimate max error in area and volume and their relative error."

Express r in terms of C: r = c/(2*pi)

V(sphere) = (4/3)*pi*^3 => c^3/(6*pi^2)
A(sphere) = 4*pi*^2 => c^2/pi


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