Question

A company is going to make a storage container with sheet steel walls. The container will be in the shape of a rectangular prism, as shown below. If the sheet steel costs $30 for each square meter, how much will the sheet steel cost in total?

Answer 1

$3060

Step-by-step explanation

Each steel sheet used for the prism costs $30 per square meter.

To find the total cost of the sheet, we have to find the surface area of the rectangular prism. Then we multiply the surface area by the cost per square meter.

The surface area of a rectangular prism is:

`\begin{gathered} A\text{ = 2(}wh\text{ + wl + hl)} \\ \text{where h = height} \\ w\text{ = width} \\ l\text{ = length} \end{gathered}`

From the diagram:

l = 7 m ; w = 3 m ; height = 3 m

Therefore, the surface area of the prism is:

`\begin{gathered} A\text{ = 2\lbrack(3 }\cdot\text{ 3) + (3 }\cdot\text{ 7) + (3 }\cdot\text{ 7)\rbrack} \\ A\text{ = 2(9 + 21 + 21)} \\ A\text{ = 2(51)} \\ A\text{ = 102 square meters} \end{gathered}`

Now, we multiply by the cost per square meter:

`\begin{gathered} C\text{ = 102 }\cdot\text{ 30} \\ C\text{ = \$3060} \end{gathered}`

That is the total cost of the steel sheet.