A cube has a surface area of 47,526 square units. What is the volume, in cubic units, of the cube?

To find the volume of the cube, we need to follow these steps:

1. Determine the surface area of one face of the cube: The surface area of a cube is given by the formula $6a^2$, where $a$ is the length of one side of the cube. Given that the total surface area is 47,526 square units, we can set up the equation: $6a^2 = 47,526$

2. Solve for $a^2$: Divide both sides of the equation by 6 to isolate $a^2$: $a^2 = \frac{47,526}{6}$ $a^2 = 7,921$

3. Solve for $a$: Take the square root of both sides to find $a$: $a = \sqrt{7,921}$ $a = 89$

4. Calculate the volume of the cube: The volume $V$ of a cube is given by the formula $a^3$. Using the value of $a$ we found: $V = 89^3$ $V = 89 \times 89 \times 89$ $V = 704,969$

Therefore, the volume of the cube is 704,969 cubic units.