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**1. Homework Statement**

The problem states: Use cylindrical coordinates to evaluate

[itex] \iiint_V \sqrt{x^2 +y^2 +z^2} \,dx\,dy\,dz [/itex]

where V is the region bounded by the plane [itex] z = 3 [/itex] and the cone [itex] z = \sqrt{x^2 + y^2} [/itex]

**2. Homework Equations**

[itex] x = r cos( \theta ) [/itex]

[itex] y = r sin( \theta ) [/itex]

[itex] z = z[/itex]

[itex] dV = dx dy dz = r dz dr d \theta [/itex]

**3. The Attempt at a Solution**

Changing to cylindrical coordinates:

[itex] \iiint_V r \sqrt{r^2 +z^2} \,dz\,dr\,d \theta [/itex]

The limits are:

[itex] 3 \le z \le r [/itex]

[itex] 0 \le r \le 9 [/itex] ???

[itex] 0 \le \theta \le 2 \pi [/itex]

I'm not sure how to tackle this integral. Attempting to evaluate it in mathematica returns an error too. To me, this question would be easier to solve using spherical polar coordinates, but the question states cylindrical.

One thing to note, [itex] \sqrt{r^2 +z^2} = R [/itex] is the equation for a sphere of radius R, in cylindrical coordinates. Not sure if this may play a part in the solution.

Any help would be greatly appreciated.