The volume of a cube is 8000 cubic feet, what is the area of its faces
A 40 square feet
B 80 square feet
C 200 square feet
D 400 square feet
well, 8000 = 20^3
20^2 = ?
To find the area of the faces of a cube, we need to know the length of one side of the cube.
The volume of a cube is calculated using the formula V = s^3, where V is the volume and s is the length of one side.
In this case, we know that the volume of the cube is 8000 cubic feet. So we can set up the equation:
8000 = s^3
To find the length of one side (s), we can take the cube root of both sides of the equation:
∛8000 = ∛(s^3)
∛8000 = s
Now, let's calculate the cube root of 8000:
∛8000 ≈ 20
So, the length of one side of the cube is approximately 20 feet.
To find the area of one face of the cube, we use the formula A = s^2, where A is the area and s is the length of one side.
Substituting the value of s (20 feet in this case), we can calculate the area:
A = 20^2
A = 400 square feet
Therefore, the area of each face of the cube is 400 square feet.
So, the correct option is D: 400 square feet.