Question

the volume of a cube is decreasing at a rate of \\(320\text{ mm}^3/\text{s}\\).

step 3 of 4: what is the formula for the surface area \\(s\\) of the cube in terms of its edge length \\(x\\)?

answer
\\(s =\\)

Explanation:

Identify the geometric properties of a cube

Using the Volume of a Cube knowledge point
A cube has six identical square faces. If the edge length of the cube is \(x\), then the area of one face is:

$$ A_{\text{face}} = x^2 $$

Express total surface area

The total surface area \(S\) is the sum of the areas of all six faces:

$$ S = 6x^2 $$

Answer:

What is the formula for the surface area \(S\) of the cube in terms of its edge length \(x\)?

\(S =\) <blank>\(6x^2\)</blank>