I was solving the following problem
Suppose I have a sphere of radius 1 metre. The sphere is colored with red and blue such that it has disconnected regions of red and blue colors.
Now I have to make a cube that fits in the sphere such that Each vertex of the cube touches a red-colored region.
This is possible if one of the following option is true
a) The aggregate area of red part is $11 m^2$ .
b) The aggregate area of red part is $10 m^2$ .
c) The aggregate area of red part is NOT $11 m^2$ .
Answer given was (a)
Where aggregate area is the sum of areas of all regions. Well I approached by calculating total surface area of sphere = $12.56 m^2$
So subtracting from $11m^2$ gives me the minimum residue and so the answer follows.
Is my reasoning correct or any other explanation for this the answer??