A rectangular box is 12 in. X 14. X 18in. What is the surface area of the largest size sphere that can fit in this box? Leave your answer in terms of pi
To find the largest size sphere that can fit in the rectangular box, we need to determine the maximum diameter of the sphere.
The diameter of the sphere should be equal to the shortest side length of the box. In this case, the shortest side length is 12 inches.
So, the diameter of the sphere is 12 inches.
The radius of the sphere is half the diameter, so the radius is 12/2 = 6 inches.
The surface area of the sphere is given by the formula A = 4πr², where r is the radius.
Plugging in the radius of 6 inches, we get:
A = 4π(6)²
= 4π(36)
= 144π
Therefore, the surface area of the largest size sphere that can fit in the rectangular box is 144π square inches.