Initially at $t = 0\,;\,h = h$ 

                $t = t\,;h = 0$

$Then,\,A\left( { - \frac{{dh}}{{dt}}} \right) = \pi {a^2}.v$

$\left[ {Velocity\,of\,efflux\,of\,liquid\,v = \sqrt {2gh} } \right]$

Integrating both sides

$\int\limits_0^t {dt =  - \frac{A}{{\sqrt {2g} \pi {a^2}}}{{\int\limits_h^0 h }^{ - 1/2}}dh} $

$\left[ t \right]_0^t =  - \frac{A}{{\sqrt {2g} \pi {a^2}}} \cdot \left[ {\frac{{{h^{1/2}}}}{{1/2}}} \right]_h^0$

$t = \frac{{\sqrt 2 A}}{{\pi {a^2}}}\sqrt {\frac{h}{g}} $