Did the cake turn out ok?
You didn't mention your baking skill level altho reading between the lines I assume you are not a pastry virgin...correct?
If you are just now learning and you still need help, answers to the following may help us help you
First the oven.
Is there a fan option?
Do you have an oven thermometer in there? (I realize you don't have lots of extra room, but temp is critical, esp for preheating)
How much actual baking room is in there? (measure to find out)
Is there a rack to set the cake pan on ?
About that pan...I was confused re the measurements (10 in length and 4 in width or 10 in round and 4 in deep)?
That may sound picky but pan size is right up there with oven specs.
My brother lives in a teeny apt and regularly bakes in his toaster oven and is almost always successful with small one layer cakes.
He told me the key to his success is to open the little door and cram the pan in as fast as he can.
If the pre-heated air drops more than 30-40 degrees ( need a thermometer for this!) he turns the temp up for about 30 seconds and then sets it back to required temp.
The reasoning behind this is that the leavening's need a blast of hot air at the get-go as this is what activates the baking powder and makes it start raising the batter.
I would check all the above before altering the written recipe.
Reasoning... it is key to make the recipe exactly as written (at least the first go round)
This will give you a baseline to start at and a point from which to add and subtract.