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

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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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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,613

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

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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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

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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