Math Is Fun Forum

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

Nehushtan

Member

Registered: 2013-03-09

Posts: 957

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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Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

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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

Stangerzv

Member

Registered: 2012-01-30

Posts: 266

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