To find the largest size sphere that can fit inside the box, we need to determine the diameter of the sphere.
The diameter of the sphere is equal to the shortest side length of the box, which in this case is 12 inches.
The surface area of a sphere with diameter d is given by the formula:
Surface Area = 4πr^2
where r is the radius of the sphere.
Since the diameter is 12 inches, the radius is half of the diameter, which is 6 inches.
Substituting the value of the radius into the formula, we get:
Surface Area = 4π(6)^2 = 4π(36) = 144π square inches.
Therefore, the surface area of the largest size sphere that can fit in the box is 144π square inches.