ANSWER
$3060
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:
[tex]\begin{gathered} A\text{ = 2(}wh\text{ + wl + hl)} \\ \text{where h = height} \\ w\text{ = width} \\ l\text{ = length} \end{gathered}[/tex]
From the diagram:
l = 7 m ; w = 3 m ; height = 3 m
Therefore, the surface area of the prism is:
[tex]\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}[/tex]
Now, we multiply by the cost per square meter:
[tex]\begin{gathered} C\text{ = 102 }\cdot\text{ 30} \\ C\text{ = \$3060} \end{gathered}[/tex]
That is the total cost of the steel sheet.
