Introduction:
To find the volume of a cube, we need to know the area of one of its faces.

Given:
Area of one face = 81 m²

Formula:
The formula for finding the volume of a cube is:
Volume = (Side length)³

Solution:
To find the volume of the cube, we need to first find the length of one side of the cube.

Step 1: Find the length of one side of the cube
We know that the area of one face is 81 m².
The area of a square is given by the formula:
Area = length x width
Since the cube has six faces and all faces are identical squares, we can find the length of one side of the square by taking the square root of the area of one face.

√81 = 9

So, the length of one side of the cube is 9 meters.

Step 2: Find the volume of the cube
Now that we know the length of one side of the cube, we can use the formula for finding the volume of a cube to find the volume.

Volume = (Side length)³
Volume = (9)³
Volume = 729

Therefore, the volume of the cube is 729 cubic meters.

Conclusion:
The volume of the cube with one face area of 81m² is 729 cubic meters.