SAT Question ba8ca563: Area and Volume answer and explanation with Desmos solution

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 $474,552$ cubic units. Substituting $474,552$ for $V$ in $V=s^3$ yields $474,552=s^3$. 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 $A=6,084$. Therefore, the area of one face of this cube is $6,084$ square units. Since a cube has $6$ faces, the surface area, in square units, of this cube is $6\left(6,084\right)$, or $36,504$.