Question
(c) Find the mass of the shell.
Mass =
A spherical shell centered at the origin has an inner radius of 5 cm and an outer radius of 8 cm. The density, delta, of the material increases linearly with the distance from the center. At the inner surface, delta=10 g/cm{}^3; at the outer surface, delta=16 g/cm^3. Using spherical coordinates, write the density, delta, as a function of radius, rho. (Type rho for rho.) delta = 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). With a = , b = , c = , d = , e = , and f = , Mass = int_a^bint_c^dint_e^f Find the mass of the shell. Mass =
Explanation / Answer
(a) density = 2 rho
(b)
a = 5
b = 8
c = 0
d = 2 pi
e = 0
f = pi
= ( 2 rho) * rho^2 * sin phi
= d rho
= d theta
= d phi
(c) integrating, we get
mass = 6942 pi grams
= 21809 g
= 21.8 kg