We have a Madeira recipe that you can use for any sized cake. It is a one egg mix that produces 15 sq.inches of cake (good enough for a 3" x 5" cake) which you just multiply up for different cake sizes.
A 10" round cake is 78.5 sq.inches (Pi R squared). Divide that by 15 and you get 5.23. If you call that 5, then you multiply this recipe by 5.
1 medium egg (5 eggs) 2ozs SR Flour (10ozs) 1oz Plain Flour (5ozs) 2oz Caster Sugar (10ozs) 2oz Butter (10ozs) zest of half a lemon (2.5lemons) 1 tsp lemon juice (5tsp)
Cream butter and sugar, then add the eggs (one at a time). You may need to add a little flour after two eggs, and a little more after four. Add lemon zest and juice, then fold in the rest of the flour. Bake in a moderate oven (160 deg.C or Gas Mark 3) for 50 - 55 minutes.
This should give you a cake of around 2 " depth. To stop it rising too much in the middle, I have heard it worth scooping the mix away from the middle towards the outside of the cake just before you put it in the oven, but I have never done that myself.
It is probably worth puting a sheet of greaseproof paper over the top at 40 mins to prevent the top drying out.