To solve for the length of each edge of the cube when its volume equals its surface area, we can follow these steps:
1. Let's denote the length of each edge of the cube by [tex]\(a\)[/tex].
2. The formula for the volume [tex]\(V\)[/tex] of a cube is given by:
[tex]\[
V = a^3
\][/tex]
3. The formula for the surface area [tex]\(A\)[/tex] of a cube is given by:
[tex]\[
A = 6a^2
\][/tex]
4. According to the problem statement, the volume is equal to the surface area:
[tex]\[
a^3 = 6a^2
\][/tex]
5. To solve for [tex]\(a\)[/tex], we need to simplify the equation. Let's divide both sides of the equation by [tex]\(a^2\)[/tex]:
[tex]\[
\frac{a^3}{a^2} = \frac{6a^2}{a^2}
\][/tex]
Simplifying further:
[tex]\[
a = 6
\][/tex]
Therefore, the length of each edge of the cube is 6 feet.
