| |
Suppose the solid in the figure is the
spherical half-shell consisting of the points above
the xy-plane that are between concentric
spheres centered at the origin of radii
cm and cm.
Suppose the density of the material
increases linearly with the distance from the
origin, and that at the inner surface
the density is
while at the outer surface it is
.
(a) Using spherical coordinates, write
as a function of . Enter as rho.
=
(b) Set up the integral to calculate the mass
of the shell in the form below. If necessary, enter
as phi, and
as theta.
A =
B =
C =
D =
E =
F =
(c) Find the mass of the shell.
| |
|