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Density is defined as (mass) divided by (volume).

The question only has meaning if it's referring to a spherical object.

The volume of the sphere is [ 4/3 pi R3 ], where [ R ] is the sphere's radius.
We're given the circumference, and we have to find [ R ].

Circumference = [ pi D ] = [ 2 pi R ].

R = (circumference) / (2 pi)

OK.

Volume = [ 4/3 pi R3 ] = [ 4/3 pi (circumference/2 pi)3 ] = [ 4/3 pi (circumference)3 / (8 pi3) ]

= (circumference)3 / (6 pi2)

And finally,

Density = (6 pi2 Mass) / (circumference)3

An ugly expression, to be sure; but that's what you get when you have a circumference and
what you need is a volume.

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โˆ™ 2009-10-28 04:47:58
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Q: What is the formula for density if you have mass and circumference?
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