The dimensions of a ball

[notquiteace]

Hello. I'd like to ask what dimensions a ball has. I was recently told that "Australia is wider than the moon". However, that did not make sense to me, as to my understanding, a ball has radius rather than width, which means that the two bodies are not directly comparible in that sense (the actual bodies, that is, rather than a spherical representation of the moon). Is this correct?

 

[tkhunny]

Though the comparison is a bit awkward, there is no reason to deny the ordering of linear measurement.

The moon is DIAMETER wide - or 2 * RADIUS wide. - or about 3,474 km
Australia is about 4,000 km, depending on exactly which two points you pick to measure.

 

[Dr.Peterson]

The main trouble is that "width" can be taken several ways. I would tend to think that in comparing regions of surfaces of spheres (the whole moon and one island on earth), areas would be the most natural comparison, but if you have to talk about width, perhaps the circumference (the farthest you can go east to west) makes most sense. That would be 11,000 km or so.

But I suppose if you just had a big pair of calipers to measure them both, rather than walking, then the diameter makes sense, though by that measure Australia would be a littler narrower (measuring a chord, not an arc).

But what's the problem with "a spherical representation of the moon"? Isn't that what you're using in talking about the radius?

 

[LCKurtz]

I would think the "calipers" interpretation might be appropriate: [MATH]\text{Diam}(S) = sup\{|x-y|: x,~y \in S\}[/MATH]

 

[tkhunny]

Less formally, if the Moon crashed into Earth, as centered as possible on Australia, with no splashing or collateral damage, just cutting a hole straight through, would any of Australia be left? Yes.