I'm struggling to understand this problem. It seems that the location of the points of the cube don't match up to make a cube.

Question

Find an equation of the largest sphere contained in the cube determined by the planes x = 2, x = 16; y = 4, y = 18; and z = 7, z = 21.

Answer 1

The center is (x = (2 + 16)/2, y = (4+18)/2, z = (7+21)/2) or (9, 11, 14), and each of the sides is 7 from the center, so it is (x-9)^2 + (y-11)^2 + (z-14)^2 = 7^2 or (x-9)^2 + (y-11)^2 + (z-14)^2 = 49

If you prefer, this may be written x^2 - 18x + 81 + y^2 - 22y + 121 + z^2 - 28z + 196 = 49 or

x^2 - 18x + y^2 - 22y + z^2 - 28z + 349 = 0