Answer:
The length of each side of the cube is [tex]\frac{1}{8}\ m[/tex]
Step-by-step explanation:
we know that
The volume of a cube is equal to
[tex]V=LWH[/tex]
but remember that in a cube
Length, width and height have the same value
so
Let
b-----> the length side of the cube
[tex]L=W=H=b[/tex]
substitute in the formula
[tex]V=(b)(b)(b)=b^{3}[/tex]
In this problem we have
[tex]V=\frac{1}{512}\ m^{3}[/tex]
substitute and solve for b
[tex]b^{3}=\frac{1}{512}[/tex]
[tex]b=\sqrt[3]{\frac{1}{512}}\\ \\b=\frac{1}{8}\ m[/tex]
therefore
The length of each side of the cube is [tex]\frac{1}{8}\ m[/tex]
