A box has a volume of 27 cubic feet. Assuming the box is a cube, what is the area of one of its faces? square feet

To find the area of one face of a cube with a volume of 27 cubic feet, we start by determining the length of one side of the cube.

1. The formula for the volume of a cube is:

[

V = s^3

]

where ( s ) is the length of one side.

2. Since the volume ( V ) is given as 27 cubic feet, we can set up the equation:

[

s^3 = 27

]

3. To find ( s ), we take the cube root of both sides:

[

s = sqrt[3]{27} = 3 text{ feet}

]

4. Now, to find the area of one face of the cube, we use the formula for the area of a square:

[

text{Area} = s^2 = 3^2 = 9 text{ square feet}

]

So, the area of one of the faces of the cube is 9 square feet.