Map scale confusion.

Now, I'm not sure where to post this, so I felt it'd be safest to do so here.

I have a bit of a problem with map scaling...and math. To make a long story short, it was a biblical miracle I ever passed math at all. Numbers and me don't mix, and so when I come across a mathematical problem I panic. This is what it is.

My 'world' is around the size of Earth, but just a bit larger. The surface area is:

150,000,000 km^2 for Land
365,000,000 km^2 for Water

And so a total of 515,000,000 km^2 for the entirety of the planet.

My goal is to work out how many km = to 1cm on the map. Apparently the proper way to do this is to work with random numbers, like 1:10000000, but I need the scale to be the exact size of earth, it's vital to the lore behind the map.

To make life easier (just a tad) I've separated this "pangea" into different continents, still, I don't think the size of the number will help at all.

The Map is being worked on an A4 sketch pad, portrait, and so is 624cm^2 in area.

If any of you are knowledgeable in this field of work, I'll thank you a thousand times over (using a gif of course xD.)

I apologise if I come across as arrogant, but this thing has been eating my coconut for days.

Thanks alot, Beron.