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.
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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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.
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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...