A spherical shell centered at the origin has an inner radius

A spherical shell centered at the origin has an inner radius of 4 cm and an outer radius of 7 cm. The density, delta, of the material increases linearly with the distance from the center. At the inner surface, delta = 11 g/cm^3; at the outer surface, delta = 20 g/cm^3. (a) Using spherical coordinates, write the density, delta, as a function of radius, rho. (Type rho for rho.) delta = (b) Write an integral in spherical coordinates giving the mass of the shell (for this representation, do not reduce the domain of the integral by using symmetry; type phi and theta for phi and theta). (c) Find the mass of the shell. Mass =

Solution

from the given information

Density = 3(radius) - 1