A rectangular box is 12 in. × 14 in. × 18 in. What is the surface area of the largest size sphere that could fit in this box? Leave your answer in terms of pi.
To find the largest size sphere that could fit in the box, we need to determine which dimension will limit the radius of the sphere.
The diameter of the sphere cannot exceed the smallest dimension of the box. In this case, the smallest dimension is 12 inches.
Therefore, the maximum diameter of the sphere is 12 inches, and the radius is half of that, which is 6 inches.
The surface area of a sphere is given by the formula A = 4πr^2, where r is the radius.
Plugging in the radius of 6 inches into the formula, we get:
A = 4π(6^2)
= 4π(36)
= 144π
Therefore, the surface area of the largest size sphere that could fit in the box is 144π square inches.