  In this article we extend the variational technique for maximal volume
estimation of a black hole developed by Christodoulou and Rovelli (CR) to the
case of a charged BTZ black hole in 2+1 dimensions. The technique involves a
study of the equation of motion of a hypothetical particle moving in an
auxiliary manifold defined by spacetime variables. We then compare this
estimation with the volume computed using maximization method and extrinsic
curvature method. The charge Q of the black hole appears as a log term in the
metric and hence an analytical solution for the volume does not exist. So first
we compute the steady state radius and the volume for limiting case when the
charge Q is very small i.e. Q << 1 and then carry out a numerical analysis to
solve for the volume for more generic values of the charge. We find that the
volume grows monotonically with the advance time. We further investigate the
functional behaviour of the entropy of a massless scalar field living on the
maximal hypersurface of a near extremal black hole. We show that this volume
entropy exhibits a very different functional form compared to the horizon
entropy.
