\(p_{1}=\frac{m_{1}g}{a^2}\)
\(\quad =\frac{\rho a^3g}{a^2}\)
\(\quad =\rho ag\)
\(p_{2}=\frac{m_{2}g}{b^2}\)
\(\quad =\frac{\rho b^3g}{b^2}\)
\(\quad =\rho bg\)
\(\frac{p_{1}}{p_{2}}=\frac{a}{b}\)
\(p_{3}=\frac{(m_{1}+m_{2})g}{b^2}\)
\(\quad =\frac{m_{1}g}{b^2}+\frac{m_{2}g}{b_{2}}\)
\(\quad =\frac{m_{1}g}{b^2}+p_{2}\)
\(\quad =\frac{m_{1}g*a^2}{ab^2}+p_{2}\)
\(\quad =\frac{m_{1}g*a^2}{a^2b^2}+p_{2}\)
\(\quad =\frac{p_{1}*a^2}{b^2}+p_{2}\)
\(\quad =\frac{p_{1}^3}{p_{2}^2}+p_{2}\)
\(\quad =\frac{p_{1}^3+p_{2}^3}{p_{2}^2}\)