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The volume of a cube is x cubic feet and its surface area is x area square feet, where x
represents the same number. Find the length of each edge of the cube

Verified Answer :

GinnyAnswer

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 \(\(a\)\).

2. The formula for the volume \(\(V\)\) of a cube is given by:
\(\[ V = a^3 \]\)

3. The formula for the surface area \(\(A\)\) of a cube is given by:
\(\[ A = 6a^2 \]\)

4. According to the problem statement, the volume is equal to the surface area:
\(\[ a^3 = 6a^2 \]\)

5. To solve for \(\(a\)\), we need to simplify the equation. Let's divide both sides of the equation by \(\(a^2\)\):
\(\[ \frac{a^3}{a^2} = \frac{6a^2}{a^2} \]\)
Simplifying further:
\(\[ a = 6 \]\)

Therefore, the length of each edge of the cube is 6 feet.

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