Determine $($a$)$ the Voigt and $($b$)$ the Reuss bounds to the modulus of elasticity of a ceramic material consisting of layers of alumina and a high$-$silica glass. The modulus of elasticity of the alumina is $380$ GPa and that of the glass is $72\mathrm{.}4$ GPa, and the glass represents $30$ vol$\%$ of the solid.