sat-dog

The correct answer is $\mathrm{36,504}$. The volume of a cube can be found using the formula $V=s^3$, where $s$ represents the edge length of a cube. It’s given that this cube has a volume of $\mathrm{474,552}$ cubic units. Substituting $\mathrm{474,552}$ for $V$ in $V=s^3$ yields $\mathrm{474,552}=s^3$. Taking the cube root of both sides of this equation yields $78=s$. Thus, the edge length of the cube is $78$ units. Since each face of a cube is a square, it follows that each face has an edge length of $78$ units. The area of a square can be found using the formula $A=s^2$. Substituting $78$ for $s$ in this formula yields $A={78}^2$, or $A=\mathrm{6,084}$. Therefore, the area of one face of this cube is $\mathrm{6,084}$ square units. Since a cube has $6$ faces, the surface area, in square units, of this cube is $6\left(\mathrm{6,084}\right)$, or $\mathrm{36,504}$.