What is a paradox?
Lets start with the easy stuff first. A paradox is an argument that produces a complete inconsistency within a logical common sense environment.
Many logical paradoxes are known to be invalid arguments as my fellow philosopher 
OK let critical thinking commence ....
Right, I'm going to think outside the box on this one for a start, so I'm going to use a mathematical paradox.
Lets look at the mathematical function:
f(x)=1xf(x)=1x with x∈[1,+∞)
If we rotate this graph around the x-axis it creates a horn shaped 3D object called 'Gabriel's horn' (Yes as in the angel!).
Using some second year University maths we can calculate the horn's volume and surface of the solid revolution and find ourselves something very paradoxical.
The solid has a volume of:
V=limt→∞π∫t1(1x)2dx=limt→∞π(1−1t)=π
and the surface:
S=limt→∞2π∫t11x1+1x4−−−−−√>S=limt→∞2π∫1t1x1+1x4>
limt→∞2π∫t1(1x)=limt→∞2πlnt=+∞
So, it appears that Gabriel's horn has an infinite surface, but only a finite volume. Very freaky!
For more on Gabriel's Horn, see Wikipedia at:
https://en.wikipedia.org/wiki/Gabriel%27s_Horn
P.S. Due to the Steemit formatting rules one mathematical symbol is missing - spot it and win 1 Steem!