Four cans are bundled together using a string. ...?

Question

If you allow 5 cm for tying the knot, what is the shortest amount of string that you need if each can has a radius of 4 cm?

Answer 1

Let r be the radius of each can.

Placing the cans together symmetrically, the distance from the centre of one can to the centre of the next going round clockwise (not diagonally) is 2r.

2r is therefore the length of the string in each position where it is not in contact with the cans.

The string goes round 1/4 of the circumference of each can, a distance of pi r / 2.

The total length of the string is therefore:

4(pi r / 2 + 2r) + 5

= 2pi r + 8r + 5

= 2r(pi + 4) + 5

= 8(pi + 4) + 5

= 8pi + 37

= 62.1 cm.

Answer 2

Not enough data. If they were very flat (tuna-can or move film shaped - for those who remember), I'd stack them and tie them as a column.