The volume of this cube is 512 cubic millimeters. What is the surface area of this cube?
To find the surface area of a cube, we need to know the length of one side. We can find the length of one side by taking the cube root of the volume:
∛512 = 8
So, the length of one side is 8 millimeters.
To find the surface area, we need to add up the areas of all six faces of the cube. Since all six faces are identical squares, we can use the formula for the area of a square:
Area of one face = 8 mm × 8 mm = 64 mm²
Total surface area = 6 × area of one face = 6 × 64 mm² = 384 mm²
Therefore, the surface area of the cube is 384 square millimeters.