$S=240000b^{2}a^{3}\text{ and }240000b^{2}a^{3}=1,b=-1$

$b=-1$
$a=\frac{30^{\frac{2}{3}}}{600}\text{ and }S=1$

$a = \frac{30 ^ {\frac{2}{3}}}{600} = 0.01609148974342716$
$S=1\text{ and }b=-1$