Answer
(a) $x^2+y^2+z^2=4$
(b) $x^2+y^2=1.75$ and $z=-1.5$
Work Step by Step
The coordinate system and the sphere is shown in the figure.
(a) With the origin at the center of the sphere of radius $R=2$ ft, the equation of the sphere can be written as
$x^2+y^2+z^2=4$
(b) Since there are six inches, or 0.5 ft submerged, the distance from the sphere center and the surface of water is $h=2-0.5=1.5$ ft. The radius of the sphere, the height $h$, and the radius of the circle $r$ (at the waterline of the buoy) form a right triangle with $r^2=R^2-h^2=4-2.25=1.75$. And the equation of the circle formed at the waterline of the buoy is given by $x^2+y^2=1.75$ and $z=-1.5$
