We wish to purchase a steel tank to store $20,000$ gallons of propane; design pressure is $250$ psig, and design stress is $20,000$ psi. What will be the weight of metal in the shell $($excluding foundations, valves, manholes, etc.$)$ if the tank is $($a$)$ cylindrical with hemispherical ends, like those in the below figures. The cylindrical section will have length $=6$ times diameter. $($b$)$ spherical. Assume that the simple thin$-$walled formulae may be used. For steel, specific gravity $=7\mathrm{.}9$