An Understanding of Muscle Size

So I recently decided to do some basic math comparing various muscle sizes. This is so that we're all on the same page as far as our perception and understanding of how large muscles actually are. If you spot an error in logic or have other questions, please let me know.

For this example I'm just going to compare 15" (38cm) biceps to 18" (46cm). At first glance, the difference between 15 and 18 is just 3 inches, which is still significant, but not as much I think as most people realize. 3" by itself added to 15" is a 20% increase, however that is only a one dimensional estimation. If you take into account the increase in area of the biceps (imagine a cross-sectional slice that resembles a circle) then the difference is much more substantial.

I'm sure everyone remembers the area of a circle is (1/2)(πr²)😉, where the r = the radius and π ≈ 3.14. To find r, we need to use the circumference (perimeter) formula, C = 2πr, and set it to r = C/(2π). Since C is 15", solving for r we get r = 2.39". Putting this value into the area formula, for 15" biceps the area A = 8.97in². For 18" biceps, the radius would be r = 2.87, and the area is A = 12.93in². So what we end up with is:

15" biceps, Area(A) = 8.97in² (22.78cm²)

18" biceps, Area(A) = 12.93in² (32.84cm²)

So comparing these two values, the two-dimensional increase from 15" to 18" is actually 44%! This knowledge, at least for me, provides a better understanding of why bodybuilders tend to plateau at certain sizes, as I imagine the amount of work/training required to gain each additional inch of mass goes up exponentially.

What do you guys think? Is this sound logic? Is it flawed? Does it make sense?

I like mathematic when it includes muscles :)

Sorry, my comment will not be as literate as yours or contain calculation.

I am curious to hear the opinions on the relation between muscle size, and the height of a person. For instance Vivi has massive 27" quads but also is quite short. Whereas I am 6'2" and have 25.5" quads and they sure dont look as full/buldgy as hers. Within this spectrum, the same could be said from Jordynne Grace and her biceps. Because she's short and has short arms...

I guess where I am getting at is: Is there any calculation to take into account the height/weight/muscle size ratio that can account for height disparity? (Or is it all in my head)

What you're referring to is mass in three-dimensions, and yes height does influence muscle size (longer limbs = longer muscles). I don't think there is a simple calculation to determine muscle size on a 3D level... if you're going to use geometric formulae, you're basically restricted to using either the sphere or cylinder (volume) equations. Otherwise to get a more precise measurement, it would involve calculus, which is not something I'm particularly interested in figuring out... although anyone else here is welcome to try.

The area example in the original post was just to give people a clearer understanding of how large muscles are likely larger than they originally thought.