\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} A solid body of uniform density
$\rho$ fills the portion of space lying in the first octant and
between two spheres centered at the origin of radus $a$ and $b$,
respectively, with $a<b$. The coordinates of points in this solid are
those which satisfy $x,y,z\ge0$ and $a^2\le x^2+y^2+z^2\le b^2$.

\medskip

\noindent a) Use integration in spherical coordinates to find the
coordinates $(\bar x,\bar y,\bar z)$ of the center of mass of this
body. (How can symmetry simplify this problem?)

\medskip

\noindent b) Find the coordinates of the center of mass when the body
becomes a very thin spherical shell---that is, find the limiting value
of the position of the center of mass from part a) as the inner
radius $a$ approaches the outer radius $b$.

\vfil\eject\end

