0

I've searched around and can't seem to find a solution to what I imagine would be a fairly simple problem. I'm trying to calculate what size a parcel bag I would need to fit in a malleable item, such as a towel.

I'd thought that I could just calculate the volume of the bag sizes, and the volume of the folded towel to determine this, but given the parcel bags are flat, that doesn't seem to work.

For instance, I have a parcel bag which is 26cm * 39cm, and I've given it a height of 1cm, a volume of 1,014cm cubed. My folded towel is 21cm * 28cm * 7cm, giving a volume of 4,116cm cubed. The folded towel fits in the bag, so where have I gone wrong?

Thanks in advance

DylanB
  • 101
  • You can open the bag. The area is the same, but the volume increases – Andrei Jul 18 '20 at 03:19
  • I guess I didn't think the volume would increase because opening the bag makes the sides come in. Obviously once the bag is open, it's not a rectangle anymore, so how would you calculate the volume? – DylanB Jul 18 '20 at 03:20

1 Answers1

1

Welcome to (one of) the disconnect(s) between mathematics/science and real life! You assumed a thickness of the bag of $1$ cm, but why that instead of $1/2$ or $2$ or something else?. I suspect the sides bulged out rather farther than that, increasing the volume. You also measured the towel in an uncompressed state and ignored the fact that the corners were round, not square. The bag and the towel found a compromise volume that suited them both.

Ross Millikan
  • 374,822
  • I was hoping to ignore the facts that the towel does indeed compress, and if pushed, the plastic bag does stretch a little. I suppose the thickness, when laid flat, would be 0, but that wouldn't get me a very big volume :( – DylanB Jul 18 '20 at 03:23
  • It is not that the plastic stretches, but that its shape is not a parallelepiped but the sides bulge going towards a sphere. If it is 6 cm in the center, the volume is much higher. My experience with towels is that you can compress them around 50%, which makes a big difference. That was the point of the first sentence. – Ross Millikan Jul 18 '20 at 03:26
  • It certainly does, but I'm happy to ignore the compression in this case (at least to begin with). So you're saying I could consider the plastic bag as a cylinder (ignoring that it's closed on one end) and work out the volume that way? – DylanB Jul 18 '20 at 03:30
  • You can't ignore the compression if you use the measured volume of the towel as a constraint. The maximum volume of the bag is complicated. It should be less than a cylinder with circumference the small dimension and height the large one, but not necessarily. It can still bulge in the middle and make more volume. A true upper bound is to consider the area of the bag (both sides) as the surface of a sphere. – Ross Millikan Jul 18 '20 at 03:34
  • Ok, I've taken your suggestion to calculate the volume of the sphere, and got the (LengthWidth) 2 to get the total surface area of the inside of the bag. I've then worked out the radius as the SQRT(SurfaceArea/(4* PI)). Finally used the radius to get the volume as (4/3)PI(radius^3). For the given dimensions of 265mm width and 385mm length, we get a volume of 8,667,197.9mm cubed. – DylanB Jul 18 '20 at 04:03
  • I then tightly rolled up the towel, which makes it a cylinder, and measured the circumference as 410mm, used that to calculate the radius as Circumference/(2 * PI). Used that radius to calculate the area of the end as PI * (radius ^2). Measured the height as 110mm, multiplied the Area by the height to get a volume of 1,471,467mm cubed – DylanB Jul 18 '20 at 04:06