anonymous
  • anonymous
How do I find the regions for the triple integral to calculate the mass of the the volume between the paraboloid x^2+y^2 = 2az and the sphere x^2+y^2+z^2=3a^2 with a density of d(x,y,z)=x^2+y^2+z^2?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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amistre64
  • amistre64
is that similar to finding the solution to a system of equations in order to compute that volume of a solid?
anonymous
  • anonymous
I didn't quite understand what you mean... To be more clear, I must find out the volume between the two objects, then calculate it's mass. (oh and a>0)
amistre64
  • amistre64
oh... so the sphere and the paraboloid arent intersecting are they...lol. Wrong concept on my part :)

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anonymous
  • anonymous
yes they are intersecting, and I must find that volume.
amistre64
  • amistre64
when two curves meet and we want to find the area between them, we integrate the bounds between where they meet; is that something we can do to the sphere and parabaloid?
amistre64
  • amistre64
when does: x^2 +y^2 -2az = x^2 +y^2 +z^2-3az^2 ?
anonymous
  • anonymous
it intersects in a circle in the plane z=a
amistre64
  • amistre64
that circle is one bound of the interecting shapes then; do we have an x bound and a ybound yet?
amistre64
  • amistre64
we are trying, if i see it correctly, find the area that is scooped out of an ice cream container :)
amistre64
  • amistre64
area means volume lol
amistre64
  • amistre64
there should be an upper and lower bound of all three dimensions
amistre64
  • amistre64
if we could extablish a cross section; could we spin it to find the volume of the solid created by the rotation about an axis?
anonymous
  • anonymous
Unusually complicated. I would try\[\int\limits_{0}^{2\pi}\int\limits_{r ^{2}/2a}^{\sqrt{3a ^{2}-r ^{2}}}\int\limits_{a \sqrt{2(3a ^{2}-1)}}^{a ^{2\sqrt{6}}}r ^{3+z ^{2}drdzd \theta}\]
anonymous
  • anonymous
thanks guys, I'll give it a try. Although I'm not so sure about the limits of dr

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