Dynamic instability of microtubules may reach the steady state with exponentially growing or decaying length distribution in a confined geometry such as a cell-like environment. In this brief communication, the target finding time for these microtubules with the stochastic polymerization in a confined geometry is compared with the reversible polymerization. It is shown that the efficiency of microtubules with increasing length distribution at the steady state depends on the location of a target. They are very efficient in finding a target located at the cell cortex, which confirms the significant biological role they play in rapidly reaching the cell cortex to change the cell shape and to coordinate a motile activity around the cell periphery.