Question $4(20$ points$)[$Problem $2\mathrm{.}46$ Textbook$]$

The cylindrical tank with hemispherical ends shown in the figure contains a volatile liquid and its

vapor. The liquid density is $800k\frac{g}{m^3},$ and its vapor density is neglegible. The pressure in the vapor is

$120$ kPa $($absolute$)$ and the atmospheric pressure is $101$ kPa $($absolute$).SGH{g}_H=13\mathrm{.}6.$

a$.$ Derive the equation to compute the distance $h.$

b$.$ Determine the magnitude of $h$ for the giving information.