vector calc prob: mass of shell cut from cone z=sqrt{x^2+y^2} by planes z=1, z=2

[djcan80]

this is the problem

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\(\displaystyle \mbox{Find the mass of a thin shell with density }\, \delta\, (x,\, y,\, z)\, =\, x^2\, \mbox{ cut from}\)

\(\displaystyle \mbox{the cone }\,z\, =\, \sqrt{\strut x^2\, +\, y^2\, }\, \mbox{ by the planes }\, z\, =\, 1\, \mbox{ and }\, z\, =\, 2.\)

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Can someone show me the work and answer?
Thank you!

 

[Deleted member 4993]

this is the problem

---

\(\displaystyle \mbox{Find the mass of a thin shell with density }\, \delta\, (x,\, y,\, z)\, =\, x^2\, \mbox{ cut from}\)

\(\displaystyle \mbox{the cone }\,z\, =\, \sqrt{\strut x^2\, +\, y^2\, }\, \mbox{ by the planes }\, z\, =\, 1\, \mbox{ and }\, z\, =\, 2.\)

---

Can someone show me the work and answer?
Thank you!

Draw an approximate sketch of cone and the bounding planes.

What are the limits of this integration?
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[djcan80]

Here is my work

Do you think it's a correct answer?
Thank you!