To find the surface area of the largest sphere that can fit inside the rectangular box, we first need to determine the diameter of the sphere, which will be limited by the smallest dimension of the box.
The dimensions of the box are:
- Length: 12 inches
- Width: 14 inches
- Height: 18 inches
The smallest dimension is 12 inches. Therefore, the diameter of the largest sphere that can fit inside the box is 12 inches.
The radius \( r \) of the sphere is half of the diameter: \[ r = \frac{d}{2} = \frac{12}{2} = 6 \text{ inches} \]
The surface area \( A \) of a sphere is given by the formula: \[ A = 4\pi r^2 \]
Substituting the value of the radius: \[ A = 4\pi (6)^2 = 4\pi \times 36 = 144\pi \]
Thus, the surface area of the largest size sphere that could fit in this box is: \[ \boxed{144\pi} \text{ in}^2 \]
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