At the risk of causing more confusion…
In going from a 100mm diameter to a 200mm diameter you doubled the diameter.
If you multiply the diameter by 2 you change the collecting area by 2 x 2 = 4. So with 4 times the area each tip will be caused by 1/4 = 0.25 as much rain as with no modification.
If you increase the original 100mm to 310mm, you have increased the collecting area by 3.1 x 3.1 = 9.61. With 9.61 times the area each tip will be caused by 1/9.61 = 0.104 as much rain as with no modification.
Does that make sense?