Question

if the number of square centimeters in the total surface area of a cube is the same as the number of cubic centimeters in its volume, what is the length of a side of the cube?
the length of one side of the cube is

Explanation:

Step1: Recall cube - formulas

Let the side - length of the cube be \(a\) (in centimeters). The volume of a cube \(V=a^{3}\), and the total surface area of a cube \(S = 6a^{2}\).

Step2: Set up the equation

Given that \(V=S\), so \(a^{3}=6a^{2}\).

Step3: Solve the equation

First, move all terms to one side: \(a^{3}-6a^{2}=0\). Factor out \(a^{2}\): \(a^{2}(a - 6)=0\). This gives two solutions for \(a\): \(a = 0\) or \(a=6\). Since the side - length of a non - degenerate cube cannot be \(0\), we discard \(a = 0\).

Answer:

6