An open rectangular box extremely measures 4m*3m*4m. Find the total cost of painting the box extremely if it costs #20.00 to paint one square meter
First, we need to find the total area to be painted.
There are 6 faces to the rectangular box, and each face is a rectangle with dimensions:
- 4m x 4m (two faces)
- 4m x 3m (two faces)
- 3m x 4m (two faces)
To find the area of one face, we just multiply length x width:
- 4m x 4m = 16m² (for two faces, total = 32m²)
- 4m x 3m = 12m² (for two faces, total = 24m²)
- 3m x 4m = 12m² (for two faces, total = 24m²)
Total area = 32m² + 24m² + 24m²
Total area = 80m²
Now, we multiply the total area by the cost per square meter:
Total cost = 80m² x #20.00/m²
Total cost = #1,600.00
Therefore, the total cost of painting the box is #1,600.00.
To find the total cost of painting the box, we first need to calculate the surface area of the box.
The surface area of an open rectangular box is the sum of the areas of its five sides (top, bottom, and four vertical sides).
Let's calculate the surface area step by step:
1. Top and bottom sides:
Since the box is rectangular and measures 4m by 3m, the top and bottom sides have the same area, which is the product of the length and width:
Area of top and bottom sides = 4m * 3m = 12 square meters
2. Four vertical sides:
The height of the box is 4m, and the length and width are 4m and 3m, respectively. So, the area of each vertical side is the product of the height and the length (or width):
Area of each vertical side = 4m * 4m = 16 square meters
Since there are four vertical sides, the total area of the four vertical sides is:
Total area of four vertical sides = 4 * (16 square meters) = 64 square meters
3. Total surface area:
To find the total surface area of the box, we need to sum the areas of the top and bottom sides and the four vertical sides:
Total surface area = 2 * (Area of top and bottom sides) + Total area of four vertical sides
= 2 * (12 square meters) + 64 square meters
= 24 square meters + 64 square meters
= 88 square meters
Now, we can find the total cost of painting the box by multiplying the total surface area by the cost per square meter:
Total cost = Total surface area * Cost per square meter
= 88 square meters * #20.00/square meter
= #1760.00
Therefore, the total cost of painting the box is #1760.