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Hi.
Let D be a region within a sphere with radius a and also bounded within the cone z = - (x^2+y^2)^0.5.
1. Describe D with inequalities in spherical as well as cylindrical coordinates.
2. With one of the two in 1., calculate the volume integral of z^2 over the region D.
3. If D where a the volume which you get when you rotate the triangle with corners in the x,z-plane at (0,0), (0,1) and (1,1) around the z-axis and its dencity is constant. At which coordinate would its center of mass be?
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