Passage: The equation of the sphere S is x^2+y^2+z^2-4x-6y-12z+k=0...

The given equation of the sphere is $x^2+y^2+z^2-4x-6y-12z+k=0$.

Comparing this with the general equation of a sphere $x^2+y^2+z^2+2ux+2vy+2wz+d=0$, we get:
$u = -2$, $v = -3$, $w = -6$, and $d = k$.

The radius of the sphere is given by $r = \sqrt{u^2+v^2+w^2-d}$.

Substituting the given values:
$8 = \sqrt{(-2)^2+(-3)^2+(-6)^2-k}$

$8 = \sqrt{4+9+36-k}$

$8 = \sqrt{49-k}$

Squaring both sides:
$64 = 49-k$

$k = 49-64 = -15$

Answer: $-15$