Is it possible to know how much the cake weighs using a specific size of cake pan before baking?
It is a question of scaling.


In chat you told us the given recipe was for a 23 cm pan.
I'll ignore height for now, assuming the same height for all pan sizes, because that can be adjusted in a second step.


The math:


The cake batter for round cakes fills a cylinder.
The volume of which is base circle area x height, ignore height as stated above.
The formula of a circle is pi x r2. As pi is constant, ignore it.
So for scaling, you only need to look at the radius (1/2 diameter) of the pans  - or even the diameters. 


Divide the desired diameter (or radius) by the original one and square the result.

-> Use that value to multiply all ingredients.

Further adjustments: 

Height scales linear - for a cake that is 1.5 times as high as the original, you need 1.5 times the batter etc.

So for your question:


  To go from a 23cm / 9in cake to a 28cm / 11in cake,
  you need (28/23)2 = 1.48 times the original recipe.


My personal gut feeling: three of those won't feed 100-150 guests.