Find the flux due to a vector crossing an open surface

[falyusuf]

Homework Statement

Attached below.

Relevant Equations

Attached below.

Question:

Equations:

My attempt:

Could someone confirm my answer please?

 

[rude man]

If $\bf A = rz~ \hat {\bf \theta}$
then $\nabla \times \bf A = (z/r)~ \hat {\bf k} - \hat {\bf r}$
and not what is given.
Different fields ??