Three cylindrical tubes with with a 12 in diameter are strapped together by a plastic band. How long is the band?Suppose that four of the same tubes are strapped together with a snugly fitting plastic band how long is the band?

Answer 1

1st part:

Visualize three identical coins touching each other to form a "triangle". What is the circumference.
(actually make the sketch using 3 quarters)

Join the centres, you will get an equilateral triangle with sides 12.
Your circumference around the outside consists of 3 straight sections, each equal to 12, plus 3 arc-lengths each equal to 1/3 of the circle circumference
so it looks like the length of the band
= 3(12) + circumference of one circle
= 36 + 12π

Now take 4 coins. If you start with a "square" arrangement, I thing the plastic band will squish them and you will have another coin tucked into one of the corners above
Do a similar analysis as before.