The x-coordinate of the center of the sphere is the midpoint of x=2 and x=16, that is (2+16)/2=18/2=9.
The y-coordinate of the center of the sphere is the midpoint of y=4 and y=18, that is (4+18)/2=22/2=11.
The z-coordinate of the center of the sphere is the midpoint of z=7 and z=21, that is (7+21)/2=28/2=14.
We also notice that the side lengths of the cube are:16-2 = 18-4 = 21-7 = 14
Thus, we have a sphere centered at (9, 11, 14) and radius R=14/2=7 units.
The equation of the sphere with radius R and center [tex](x_0, y_0,z_0)[/tex] is given by:
[tex] (x-x_0)^{2}+ (y-y_0)^{2}+ (z-z_0)^{2}= R^{2} [/tex]
Thus the equation of the largest sphere contained in the box is:
[tex] (x-9)^{2}+ (y-11)^{2}+ (z-14)^{2}=7^{2} [/tex]
