To find the surface area of the largest sphere that can fit inside a rectangular box, we first need to determine the diameter of that sphere. The largest sphere that can fit inside the box will have a diameter equal to the smallest dimension of the box.
The dimensions of the box are:
- Length: 18 inches
- Width: 14 inches
- Height: 12 inches
The smallest dimension is 12 inches, meaning the diameter of the largest sphere that can fit in the box is also 12 inches. Therefore, the radius \( r \) of the sphere is half of the diameter:
\[ r = \frac{12}{2} = 6 \text{ inches} \]
Next, we can use the formula for the surface area \( A \) of a sphere:
\[ A = 4\pi r^2 \]
Substituting in the radius:
\[ A = 4\pi (6)^2 \]
Calculating \( (6)^2 \):
\[ (6)^2 = 36 \]
Now substituting this back into the area formula:
\[ A = 4\pi \times 36 = 144\pi \]
Thus, the surface area of the largest sphere that could fit in the box is
\[ \boxed{144\pi} \text{ square inches.} \]