1)

The following series:

is divergent. The stack would be infinitely high.

2)

Surface Area = 4*pi*r^2

-> Total surface area =

This is the famous harmonic series. Also divergent. So surface area is infinite.

3) You can probably see where this one will lead. Since volume is proportional to r^3, you will have an overharmonic series which will converge:

cubic meters

-> Weight = 10.94 newtons

Thus, infinite height, infinite surface area, finite weight.