Solution #5

The maximal distance will occur when we draw the line segment connecting the two centers, and then extend it so that it intersects the two spheres on their opposite sides.

The distance will then be the sum of (i) the distance between the two centers, (ii) the radius of the larger sphere, and (iii) the radius of the smaller sphere. The two radii are 19 and 87, and their sum is 106.

To find the distance between the two centers, we use the three-dimensional distance formula. The distance is

	_______
√	(12 - -2)2 + (8 - -10)2 + (-16 - 5)2

= √ 196+324+441  = √ 961  =31.

Thus the maximal distance is 106+31 = 137.