A sheet of cardboard measures 9 feet by 6 feet. Gina makes the entire sheet of cardboard into a closed box that is a perfect cube. What is the surface area of the box?

Well, Gina certainly has some serious cube-making skills! Now, let's calculate that surface area. Since she made a cube, all sides must be equal. We need to find the length of one side so we can calculate the surface area.

Since the length and width of the cardboard are 9 feet and 6 feet respectively, we can take the smaller dimension, which is 6 feet, as the length of a side of the cube.

Now, to find the surface area of the cube, we need to calculate the area of all six faces and add them up. The formula for the surface area of a cube is 6 times the area of one face.

The area of one face is simply the length of one side squared. So, 6 feet squared is 36 square feet.

Now, multiplying this by 6, we get 216 square feet.

So, Gina's cube has a surface area of 216 square feet. That's a whole lot of cardboard!

To find the surface area of the box, we first need to determine the dimensions of the cube.

Since the cardboard measures 9 feet by 6 feet, we can find the length of one side of the cube by taking the square root of the area of the cardboard.

The area of the cardboard is 9 feet * 6 feet = 54 square feet.

Taking the square root of 54 square feet gives us the length of one side of the cube:

Side length = √54 = 7.35 feet (rounded to two decimal places)

Since a cube has all sides equal in length, each side of the cube will be 7.35 feet.

Now, let's calculate the surface area of the cube using the formula: Surface Area = 6 * (side length)^2.

Surface Area = 6 * (7.35 feet)^2 = 6 * 53.92 square feet = 323.54 square feet (rounded to two decimal places).

Therefore, the surface area of the box is approximately 323.54 square feet.

To find the surface area of the box, we first need to determine the dimensions of the cube. Since the sheet of cardboard measures 9 feet by 6 feet, we want to find the length of each side of the cube.

To do this, we need to find the volume of the cardboard sheet and then calculate the side length of the cube using the formula for the volume of a cube.

The volume of the cardboard sheet can be found by multiplying its length, width, and height.

Volume = Length × Width × Height
= 9 ft × 6 ft × 0.01 ft (converting the height to feet)

Simplifying this, we get:

Volume = 0.54 ft³

Now, since the box is a perfect cube, all sides have the same length. Let's call the side length "s."

To find the side length of the cube, we can use the formula for volume:

Volume = s³

We can substitute the value of the volume we found earlier into this equation:

0.54 ft³ = s³

To solve for s, we need to take the cube root of both sides:

s = ∛(0.54 ft³)

Calculating this, we get:

s ≈ 0.82 ft

Now that we know the side length of the cube, we can find its surface area.

The surface area of a cube is given by the formula:

Surface Area = 6s²

Plugging in the side length we found:

Surface Area = 6(0.82 ft)²

Calculating this, we get:

Surface Area ≈ 6.3804 ft²

Therefore, the surface area of the box is approximately 6.3804 square feet.