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 can fit inside the rectangular box, we need to find the smallest dimension of the box, since the sphere can fit inside the box without overlapping any edges.
The smallest dimension of the rectangular box is 12 inches. This is the diameter of the sphere.
The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2, where r is the radius of the sphere.
The radius of the sphere is half of the diameter, so it is 12 inches / 2 = 6 inches.
Plugging the radius into the formula, we get:
Surface Area = 4π(6 in)^2 = 4π(36 in^2) = 144π in^2.
Therefore, the surface area of the largest size sphere that could fit in the rectangular box is 144π square inches.