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Feb19-12, 02:17 AM
P: 4
1. The problem statement, all variables and given/known data

Ok, so I am going to French University, I have to translate in English.

There is a hemisphere with the radius of 2. Inside of it, there is an empty space shaped as a cylinder with the radius (a< 2) which is perpendicular to the base of the hemisphere. The density of each point is different. Note that the farthest point from the base is 4.

a) Find the mass using cylinder coordinates (do not evaluate the integral)

b) Find the mass using sphere coordinates (do not evaluate the integral)

2. Relevant equations

3. The attempt at a solution

The equation of the sphere is x^2+y^2+z^2=2 where z >= 0

For a) we have to find the density equation with the given situation.

p(x,y,z) = 2(x^2 + y^2 +z^2-2)

now we have to find the interval. Before that we should change
x to rcos(theta)
y to rsing(theta)
z = z

r must be a <= r <= 2
theta must be 0 <= theta <= 2*pi
and the interval of z must be

(2-a^2)^(1/2) <= z <= 2 coz x^2+y^2=a^2

Am I right?? I feel dumb,,,

and I have no idea how to do b)

Please can you help me out? Thank you
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