So a sphere of 2m radius has a surface of about 50 m^2.
A 1000 lumen bulb illuminates the sphere with app 1000 lm / 50 m^2 = 20 lux (not 50 lux as OP wrote).
So the calculation is a bit off. OTOH if we had bulbs that shine downwards only it would be sufficient to just divide by the floor. So 100,000 lm in a 10m^2 room gets you 10,000 lux.
So a sphere of 2m radius has a surface of about 50 m^2.
A 1000 lumen bulb illuminates the sphere with app 1000 lm / 50 m^2 = 20 lux (not 50 lux as OP wrote).
So the calculation is a bit off. OTOH if we had bulbs that shine downwards only it would be sufficient to just divide by the floor. So 100,000 lm in a 10m^2 room gets you 10,000 lux.