  In this article, we aim at obtaining the analytical expressions ({\bf not
previously found and not recorded in the literature}) for the exact curved
surface area of a hemiellpsoid in terms of Appell's double hypergeometric
function of first kind. The derivation is based on Mellin-Barnes type contour
integral representations of generalized hypergeometric function$~_pF_q(z)$,
Meijer's $G$-function and analytic continuation formula for Gauss function.
Moreover, we obtain some special cases related to ellipsoid, Prolate spheroid
and Oblate spheroid. The closed forms for the exact curved surface area of a
hemiellpsoid are also verified numerically by using {\it Mathematica Program}.
