Liquid $A$ and liquid $B$ are mixed together in the ratio $4: 11$ by volume to make liquid $C$. Liquid $A$ has density $1.05 \mathrm{~g} / \mathrm{cm}^{3}$ Liquid $B$ has density $1.27 \mathrm{~g} / \mathrm{cm}^{3}$ A cylindrical container is filled completely with liquid $C$. The cylinder has radius $5 \mathrm{~cm}$ and height $20 \mathrm{~cm}$. Work out the mass, in $\mathrm{g}$, of the liquid in the container. Give your answer correct to 3 significant figures. You must show all your working.

Step 1 ：Find the volume of the cylinder: \(V = \pi r^2 h = \pi (5)^2 (20) = 1570.80 \mathrm{cm}^3\)

Step 2 ：Find the volume of liquid A and liquid B in the cylinder: \(V_A = \frac{4}{15} V = 418.88 \mathrm{cm}^3\) and \(V_B = \frac{11}{15} V = 1151.92 \mathrm{cm}^3\)

Step 3 ：Find the mass of liquid A and liquid B in the cylinder: \(m_A = \rho_A V_A = 1.05 (418.88) = 439.82 \mathrm{g}\) and \(m_B = \rho_B V_B = 1.27 (1151.92) = 1462.93 \mathrm{g}\)

Step 4 ：\(\boxed{\text{Final Answer:}}\) Add the mass of liquid A and liquid B to find the total mass of liquid C in the cylinder: \(m_C = m_A + m_B = 439.82 + 1462.93 = \boxed{1900 \mathrm{g}}\)