Answer:

Step-by-step explanation:
Since the height isn't given, we assume it to be "h" (of cylinders). And the answer will be in terms of "r" and "h".
The area of 1 arm is given, so the area of 2 arms would be:

Now, area of 2 cylinders would be the formula:

So, total area is A_arm PLUS A_cyl. The fractional area the arms are would be gotten by taking expression A_arm divided by A_total.
Shown below:

We simplify further:

THis is the answer.
So we see the ratio of the sides of two similar octagons is 2:5 so let's say the first octagon has a side of 2 and the other has a side of 5. 2*8 = 16 and 5*8 = 40. 16:40 = 4:10 = and is again 2:5. So the answer is 2:5.