Sure, let's break down the problem step-by-step:
### Step 1: Understanding the Problem
We need to wrap six identical gift boxes that are each shaped like a cube with side lengths of 6 inches. Stephanie has a roll of wrapping paper that is 30 inches wide and 10 feet long.
### Step 2: Dimensions of One Box
Each gift box is a cube with a side length of 6 inches. Therefore, each face of the cube is a square with the dimensions of 6 inches by 6 inches.
### Step 3: Surface Area of One Box
A cube has 6 faces, each with the same dimensions.
- The area of one face (square) of the cube = side_length side_length = 6 inches 6 inches = 36 square inches.
- The total surface area of one cube = 6 (area of one face) = 6 36 square inches = 216 square inches.
### Step 4: Total Surface Area for Six Boxes
Stephanie has six such boxes:
- Total surface area needed for 6 boxes = 6 (surface area of one box) = 6 216 square inches = 1296 square inches.
### Step 5: Dimensions of the Wrapping Paper
The wrapping paper is 30 inches wide and 10 feet long.
- Convert the length from feet to inches: 10 feet 12 inches/foot = 120 inches.
- Therefore, the dimensions of the wrapping paper are 30 inches wide and 120 inches long.
### Step 6: Area of the Wrapping Paper
The total area of the wrapping paper = width length = 30 inches * 120 inches = 3600 square inches.
### Step 7: Drawing the Net of One Box
To visualize the net of a cube:
- Imagine unfolding the cube into 2D space, there will be 6 square faces.
- Each square face measures 6 inches by 6 inches.
Here is an example illustration of the net of a cube:
```
[Top Face]
--------------------------------------
| 6 in | 6 in | 6 in |
------------ ------------ ------------
| 6 in | 6 in | 6 in |
--------------------------------------
| 6 in | 6 in | 6 in |
------------ ------------ ------------
[Bottom Face]
```
Each of the squares is labeled with its dimensions of 6 inches by 6 inches.
This net shows one way to unfold the cube such that all six faces are laid out in a two-dimensional plane. There are multiple correct ways to arrange these squares in a net form, but the key point is that each face is a 6" by 6" square.
### Conclusion
- Each gift box has a total surface area of 216 square inches.
- To wrap all six boxes, Stephanie needs a total of 1296 square inches of wrapping paper.
- The roll of wrapping paper is 30 inches by 120 inches, which provides 3600 square inches of wrapping paper, enough to wrap all six boxes.
This detailed breakdown should help illustrate the solution and drawing of the net for wrapping one of Stephanie's gift boxes.
