CLYINDRICAL coordinates of volume bound by z=r and z^2+y^2+x^2=4

[Unemployed]

Homework Statement

Find the smaller volume bound by cone z=r and sphere z^2+y^2+x^2=4 using cylindrcal coordinates

Homework Equations

dV=r-dr d-theta dz

The Attempt at a Solution

Limits on r: z to sqrt (4-z^2)
limits on theta: 2pi to 0
limits on z: 2-0

Did this and got 8 pi, not the same answer with spherical.
Need guidance on limits.

 

[tiny-tim]

Hi Unemployed!

(have a theta: θ and a pi: π and a square-root: √ and try using the X² icon just above the Reply box )

Limits on r: z to sqrt (4-z^2)

Not for the cone bit

 

[Unemployed]

Hi Unemployed!

(have a theta: θ and a pi: π and a square-root: √ and try using the X² icon just above the Reply box )


Not for the cone bit

For r = 0 to √2 ?

 

[tiny-tim]

No, the limit for r will still depend on z, but linearly instead of "curvily".