A company made a storage container with sheet steel walls. The container was in the shape of a rectangular prism, as shown below. Suppose the total cost of the sheet steel was $8384 . How much did the sheet steel cost per square meter?
To find the cost per square meter of the sheet steel, we first need to find the total surface area of the rectangular prism.
A rectangular prism has 6 faces - 2 rectangular faces for the top and bottom, and 4 rectangular faces for the sides.
Let's denote the length, width, and height of the rectangular prism as L, W, and H respectively.
The total surface area of the rectangular prism is given by:
Surface Area = 2(LW + WH + HL)
Given that the total cost of the sheet steel is $8384, and the cost per square meter is to be found, let's denote the total surface area of the rectangular prism as T.
Therefore, the cost per square meter can be calculated as:
Cost per square meter = Total cost / Total surface area
So, we can rewrite the formula above to solve for the total surface area:
Total surface area = Total cost / Cost per square meter
Now, we need to calculate the total surface area of the rectangular prism using the given dimensions and the formula for the surface area.
Assuming the dimensions of the rectangular prism are L = 5 meters, W = 3 meters, and H = 4 meters.
Substitute the values into the formula:
Surface Area = 2(5*3 + 3*4 + 4*5)
Surface Area = 2(15 + 12 + 20)
Surface Area = 2(47)
Surface Area = 94 square meters
Now, we can find the cost per square meter:
Cost per square meter = $8384 / 94 square meters
Cost per square meter = $89.19
Therefore, the cost of the sheet steel per square meter is $89.19.