Mathematical formula

[cathyang]

What is the formula for calculating the number of oranges measuring 1.5" each, in a large vase measuring 72" in height with a base width of 18" and its rim width of 30". The vase has a two-side indentation measuring 36" in length and 12" in width.

[gen2]

One and a half inch oranges ! ! ! (That's the diameter I presume?) You've been short changed there, my oranges are at least twice that - I'd take them back and ask for my money back.

[janetsflower]

tip them out and count them

[gen2]

This seems to be your first and only post, so welcome to AB cathyang .

But in that case, why aren't you GREEN like the rest of them?

[THECORBYLOON]

Maybe it's a coded message...

[mibn2cweus]

About tree hunerd, with some poken out the top cuz of them dents.

duhh I recon

[cathyang]

Thanks for your help, but this is no coded message nor can I tip it out to count coz its on paper. Do supply me the formula, please. Tried the duhh I recon site ,helpful but ain't there. Thanks anyway

[jake-the-peg]

You can't have a simple mathematical formula for an odd shape like that to give you an exact answer.

You can get pretty close by considering the volume of the vase, the volume of the spheres and the packing fraction.

so N x (volume of sphere) = packing fraction x volume of vase.

I can't quite picture the vase with the indentations - without them you'd have an average width of 24" so pi R squared gives you an average area of 452 square inches with a height of 72" gives you a volume of 32752 cubic inches

the volume of your "oranges" is of course 4/3 pi R cubed or .56 cubic inches (I assume that you mean a diameter of 1.5")

There are different ways to pack spheres see here:
http://mathworld.wolfram.com/SpherePacking.htm l

In random packing the packing fraction is 0.64

So N=32752*0.64/0.56 =34,731

You'd need to do a similar calculation but account for the reduction in volume due to theses indentations

[Clanad]

I had tried the Archimedes inspired approach as well, jake, but soon ran into trouble with the fact that the cylinder is not a true cylinder, as you've alluded to. I focused on the fact that the base is 18" in diameter, while the top, or "rim" is 20"... it would take some caluclations (I don't have my slide rule) to determine the average volume of the cylinder, as well as consider your question about the indentations... so... no help at all...

[Clanad]

Ooops, it's a 30" top or rim...

[Peter Pedant]

Your vase sounds like a truncated cone, volume pi r 2 ( H-h)
so that maybe the formula they want

then the indentation is a triangular prism, but I cant quite imagine that , that volume is the area of the triangle times its length.

so you subtract that

then calculate the volume of the orange

divide that into the vol of the vase, and lop off a third, because even the most efficient packing is only 68% - I thoguht it was hexgonal close packing but perhaps not.

SO it is not just one formula - but the course you are doing is not basic math so dont worry about that.

[bernardo]

The volume of one orange is 1.77 cubic inches, not 0.56 as erroneously stated above

[jake-the-peg]

Ah yes I was hurrying out the door and missed the pi.

I think the method's good though but without a clear picture of the vase I think we're all a bit stuffed on this one