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 surface area of the largest sphere that could fit in the rectangular box, we need to find the largest sphere that can fit within the rectangular box.
The diameter of the sphere should be equal to the smallest dimension of the rectangular box. In this case, the diameter of the sphere should be 12 inches.
The radius of the sphere is half of the diameter. So, the radius of the sphere is 12/2 = 6 inches.
The formula to find the surface area of a sphere is A = 4πr², where A is the surface area and r is the radius.
Plugging in the radius we found, we get A = 4π(6²) = 4π(36) = 144π.
Therefore, the surface area of the largest size sphere that could fit in the rectangular box is 144π square inches.