(c) Find the mass of the shell. Mass = A spherical shell centered at the origin

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

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