ok had to look up surface area of a sphere, it is 4 pi r squared.
so surface area of the sphere is 4 x 3.14159 x 93000000 x 93000000 = 108686539457784000 square miles
I assume then that you are talking about a direct shadow cast by earth or sun without any refraction which would, forgive me if I am mistaken, be the area of a circle with a diameter equal to either the earth or sun.
area equals pi r squared so for earth equals 3.14159 x (7926 miles / 2) and then squared = 49339871
So 49339871/108686539457784000 = 4.5396488 x 10 to the -8?
Am I close??
If not then now I know why I didn't stay at Uni long :-)