# Can anyone explain intuitively why increasing the circumference by 1 meter always increases the radius by 15.9cm?

I found the mathematical proof, and it is obviously correct. But how can the increase in radius be constant regardless of the starting circumference? With a very small circle, the increase should be huge but with a massive circle, the difference should end up miniscule shouldnt it? After all, the 1 m is getting distributed over a much larger circumference

Let the radius of the sphere be R and the new radius be R', hence

$2\pi R' = 2 \pi R + 1$

or,

$2\pi(R'-R) = 1$

or, the height $R' - R$ is $1/{2\pi} = 15.9 cms.$

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## migrated from physics.stackexchange.comJul 21 '13 at 15:42

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I think the physical reasoning will still be mathematical! –  Ali Jul 21 '13 at 15:34
Yeah, I'm not entirely sure if this is appropriate for Physics.SE. It seems to be asking for intuitive mathematical reasoning (!= physical reasoning) –  Manishearth Jul 21 '13 at 15:42
@Ali I was coming from the POV that this would be related to Newtonian Physics. But yeah, math does make more sense –  user87166 Jul 24 '13 at 14:09