A rectangular box is 12 in. x 14in. x 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.

Answer 1

To find the maximum size sphere that can fit inside the rectangular box, we need to find the maximum diameter of the sphere. The diameter of the sphere should be equal to the smallest side length of the box.

In this case, the smallest side length is 12 inches. Thus, the maximum diameter of the sphere would be 12 inches.

The surface area of a sphere is given by the formula:

Surface Area = 4π r^2

Where r is the radius of the sphere. The radius is half of the diameter, so in this case, it would be 12/2 = 6 inches.

So, the surface area of the largest size sphere that could fit in this box would be:

Surface Area = 4π(6^2)
Surface Area = 4π(36)
Surface Area = 144π

Therefore, the surface area of the largest size sphere that could fit in this box is 144π square inches.