Keiko is going to build a large wooden storage box. The box will be in the shape of a rectangular prism, as shown below. She wants to cover all the sides of the box with special wallpaper that costs $5 per square foot. How much will the wallpaper cost in total?
To calculate the total cost of the wallpaper, Keiko needs to find the total surface area of the box and then multiply it by the cost of the wallpaper per square foot.
The box has 6 sides:
- 2 sides that are length x height
- 2 sides that are width x height
- 2 sides that are length x width
Given that the box dimensions are length = 4 ft, width = 3 ft, and height = 5 ft, we can calculate the surface area of each side:
1. Side 1 and 2: 4 ft x 5 ft = 20 sq ft each (2 sides)
2. Side 3 and 4: 3 ft x 5 ft = 15 sq ft each (2 sides)
3. Side 5 and 6: 4 ft x 3 ft = 12 sq ft each (2 sides)
Now, add up the total surface area of all sides:
Total surface area = 20 sq ft + 20 sq ft + 15 sq ft + 15 sq ft + 12 sq ft + 12 sq ft
Total surface area = 94 sq ft
Now, multiply the total surface area by the cost of the wallpaper per square foot:
Total cost = 94 sq ft x $5/sq ft = $470
Therefore, the total cost of the wallpaper to cover all the sides of the box will be $470.