A cube is a 3 dimensional object with 6 square faces. All its sides are the same length, there fore the volume is equal to [tex]s^3[/tex] where s is the side length.
[tex]s^3 = \frac{27}{64} [/tex]
To solve for s, take the cube root of both sides.
[tex] \sqrt[3]{s^3}= \sqrt[3]{ \frac{27}{64} } [/tex]
[tex]s= \frac{3}{4} [/tex] feet
