Question 1178047
<a href="https://imgbb.com/"><img src="https://i.ibb.co/G5Jb6jr/cube.png" alt="cube" border="0"></a>


{{{a}}} = side lengths
{{{f}}} = face diagonal
{{{d}}} = solid diagonal
{{{S}}} = surface area
{{{V}}} = volume


Volume of a cube:

{{{V = a^3}}}

given face diagonal {{{f=8&1/4=8.25}}}

side {{{a}}}length:

 {{{2a^2=8.25^2}}}
{{{2a^2=68.0625}}}
{{{a^2=68.0625/2}}}
{{{a^2=34.03125}}}
{{{a=sqrt(34.03125)}}}
{{{a=5.833630944789017}}}

{{{V = (5.833630944789017)^3}}}
{{{V = 198.52575308985124}}}

Answer:

{{{V = 198.525753in^3}}}