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I have this problem:

Compute volume of solid bounded by these planes:

[tex]

z = 1

[/tex]

[tex]

z^2 = x^2 + y^2

[/tex]

When I draw it, it's cone standing on its top in the origin and cut with the [itex]z = 1[/itex] plane.

So after converting to cylindrical coordinates:

[tex]

x = r\cos \phi

[/tex]

[tex]

y = r\sin \phi

[/tex]

[tex]

z = z

[/tex]

[tex]

|J_{f}(r,\phi,z)| = r

[/tex]

I get

[tex]

0 \leq z \leq 1

[/tex]

[tex]

0 \leq \phi \leq 2\pi

[/tex]

[tex]

0 \leq r \leq 1

[/tex]

And

[tex]

V = \iiint_{M}\ dx\ dy\ dz\ =\ \int_{0}^{2\pi}\int_{0}^{1}\int_{0}^{1} r\ dr\ dz\ d\phi

[/tex]

But I got [itex]\pi[/itex] as a result, which is obviously incorrect :(

Can you see where I am doing a mistake?

Thank you!

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# Homework Help: Volume of a cone

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