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## #1 2013-04-10 01:30:32

harmonique
Member
Registered: 2013-04-10
Posts: 2

### radius 3 mystery

Hi

A sphere with radius 3 has an area of 113.0973 squared and a volume of 113.0973 cubed. The numbers are the same. Can anyone tell me why this is. It only happens with a radius of 3 or 30, 300 etc.

I suspect it has something to do with PI being close to 3.

Cheers
HM

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## #2 2013-04-10 03:02:31

Nehushtan
Member
Registered: 2013-03-09
Posts: 913
Website

### Re: radius 3 mystery

It only happens when r = 3. This is because

so

. Hence the surface area and the volume of a sphere are numerically equal if and only if its radius is 3.

PS: It has nothing to do with the value of pi.

Last edited by Nehushtan (2013-04-10 03:10:38)

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## #3 2013-04-10 05:56:14

bob bundy
Registered: 2010-06-20
Posts: 8,322

### Re: radius 3 mystery

hi harmonique

Welcome to the forum.

As Nehushtan says r = 3 is the only time this happens.

Check your arithmetic if you're getting r = 30 and r = 300 as solutions too.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #4 2013-04-10 11:02:41

harmonique
Member
Registered: 2013-04-10
Posts: 2

### Re: radius 3 mystery

Hi guys,

Thanks for your replies.

Yes i see what you mean... it only works for radius 3.

I like to ponder the significance of a mathematical event like this as it's similar to Kepler's third law
(sidereal periods of the planets squared equals distance of the planets cubed). I wasn't aware that this was also true for a sphere with radius 3. There may not be anything in it but i was just wondering...

HM

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## #5 2013-04-10 14:20:43

Stangerzv
Member
Registered: 2012-01-30
Posts: 255

### Re: radius 3 mystery

There is nothing mystery though. Here is why:

Let A=V

Rearranging the equation above yields,

So, r=0 or 3

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