$(20$ pts$.)$ For the steelmaking furnace schematically shown below, pressure inside the bubble is given as $1\mathrm{.}5$atm for the mechanical equilibrium case. If the total pressure above the slag is $0\mathrm{.}3$atm, then calculate the depth of the slag layer $($i$.$e$.x=?).$

${}_{\text{m}\text{e}\text{a}\text{l}}=7\frac{g}{c}{m}^3,{}_{\text{s}\text{l}\text{a}\text{g}}=2\mathrm{.}5\frac{g}{c}{m}^3,$ Surface tension for steel, ${}_{\text{s}\text{t}\text{e}\text{e}\text{l}}=1500dyn\frac{e}{c}m,$ take radius of bubble as $r=100m,g=981c\frac{m}{s^2}$

dyne $=1g*\frac{cm}{s^2}$ and $1$atm$=1013250$ dyne $\{\frac{\text{:}}{c}{m}^2)$