Problem $10\mathrm{.}084-$ Composite Body Made$-$up of Slender Rods

An object is constructed by welding together three small$-$diameter uniform identical rods, each having quarter$-$circular shape and $0\mathrm{.}53$ Ib weight. Determine the mass moment of inertia of the object about the $\backslash ($ x $\backslash )$ axis. $($Round the final answer to four decimal places.$)$

The mass moment of inertia of the object about the $\backslash ($ x $\backslash )$ axis is $\backslash (\mathrm{.}4612\backslash$boldsymbol$\{$x$\}\backslash )$ slug.in$.\backslash (\{\}^\{2\}\backslash )$