Step 1: Understand the formula for cube space diagonal

The space diagonal $d$ of a cube with edge length $a$ is given by $d = a\sqrt{3}$. Squaring both sides gives the square of the space diagonal: $d^2 = 3a^2$.

$d^2 = 3a^2 = 2175$

Step 2: Relate total surface area to $a^2$

The total surface area $S$ of a cube with 6 square faces of side $a$ is $S = 6a^2$.

$S = 6a^2$

Step 3: Calculate the total surface area

Since $3a^2 = 2175$, we can find $6a^2$ by multiplying by 2: $S = 2 \times 3a^2 = 2 \times 2175 = 4350 \text{ cm}^2$.

$S = 2 \times 2175 = 4350 \text{ cm}^2$