To determine the amount of cardboard Kabelo needs to build a box with the given dimensions, we need to calculate the total surface area of the box. The box has six faces: two for each pair of dimensions (length and width, length and height, and width and height). Let's calculate the area for each pair of faces and then sum the areas to find the total amount of cardboard needed.
The given dimensions of the box are:
- Length = 12 meters
- Width = 8 meters
- Height = 10 meters
Let's proceed step-by-step:
1. Calculate the area for each pair of faces:
- Length and Width:
The area of one face with length and width is:
```
Area_length_width = Length Width
```
Substituting the values:
```
Area_length_width = 12 meters 8 meters = 96 square meters
```
- Length and Height:
The area of one face with length and height is:
```
Area_length_height = Length Height
```
Substituting the values:
```
Area_length_height = 12 meters 10 meters = 120 square meters
```
- Width and Height:
The area of one face with width and height is:
```
Area_width_height = Width Height
```
Substituting the values:
```
Area_width_height = 8 meters 10 meters = 80 square meters
```
2. Calculate the total surface area:
Each of these face areas will appear twice on the box (since the box has opposite faces that are identical).
So, the total cardboard needed is:
```
Total_cardboard = 2 (Area_length_width + Area_length_height + Area_width_height)
```
Substituting the calculated areas:
```
Total_cardboard = 2 (96 square meters + 120 square meters + 80 square meters)
```
Performing the final calculations:
```
Total_cardboard = 2 * 296 square meters = 592 square meters
```
Therefore, Kabelo needs 592 square meters of cardboard to build the box.
