The volume of a cube is 125 dm, find the area of one of its faces.

The volume of the cube is 125 dm ^ 3.
Let’s determine the area of its face.
Since this is a cube, all its sides are equal. We find the volume of the cube by the following formula.
V = a ^ 3.
That is, in order to find the volume, we multiply the length by the width and by the height.
Further, knowing the volume, we find the side of the cube.
a ^ 3 = V.
a = V ^ 1/3.
a = 125 ^ 1/3 = (5 ^ 3) ^ 1/3 = 5 ^ (3 × 1/3) = 5.
The side of the cube is 5 in. Find the area of the face.
S = a ^ 2 = 5 ^ 2 = 25 dm ^ 2.
This means that the face area is 25 dm ^ 2.
Answer: the area of a cube face is 25 dm ^ 2.