  In this paper, we study approximate cloaking for the Helmholtz equation in 3d
where the cloaking device is based on transformations which blow up a cylinder
of fixed height and small cross section of radius $\eps$ into the cloaked
region. Assuming the zero Dirichlet boundary condition is imposed on the
boundary of the cloaked region, we show that the degree of visibility is of
order $\eps$ as $\eps$ goes to 0. This fact is quite surprising since it is
known that the degree of visibility, for the scheme using transformations which
blow up a small region of diameter $\eps$ into the cloaked region, is of order
$\eps$ in 3d and $1/ |\ln \eps|$ in 2d. To understand the relation between
these contexts, we as well revisit the known estimates and show that the degree
of visibility is of order $\eps^{d-1}$ ($d=2,3$) for the scheme using
transformations which blow up a small {\it ball} of diameter $\eps$ into the
cloaked region as long as the zero Dirichlet boundary condition is imposed on
the boundary of the cloaked region. The symmetry of the cross section and of
the ball are crucial so that these results hold.
