  This work provides an exact mathematical characterization of the meniscus
formed by a liquid of density $\rho$ (model for tumor tissue) when probed with
a cantilever device, operating by gravity (acceleration $g$) and with surface
tension coefficient $\sigma$ (material-dependent for the specific choice of
liquid and cantilever). The shape and extremal parameters (maximum height
$\mathcal{H}$, break-off volume $\mathcal{V}$) of the meniscus formed, as
functions of $\sigma, \rho$, are found by an exact analysis. Having knowledge
of the explicit relationship between these parameters allows to perform in one
procedure both diagnosis and treatment.
