Erin needs to spend [tex]\$\text{ }41.44[/tex] on the contact paper to cover the box completely.
Further explanation:
The given length, breadth and height of the box is [tex]\text{11 inches, 9 inches}[/tex] and [tex]\text{8 inches}[/tex] respectively.
The cost of the contact paper is [tex]\text{8 cents}[/tex] per square inch therefore the cost in dollars for the contact paper will be [tex]\fbox{\begin{minispace}\\\ 8\times {0.01}=\$ \text{ }0.08\end{minispace}}[/tex].
Let the length, breadth and height of the rectangular prism box be [tex]l, b[/tex] and [tex]h[/tex] then,
[tex]l=11\\b=8\\ h=9[/tex]
The area of a rectangular prism is defined as,
[tex]\fbox{\begin{minispace}\\A=2(l\times b+ b \times h+ h \times l)\end{minispace}}[/tex]
So, the total surface area of the box [tex]A[/tex] is obtained as,
[tex]A=2( 11\times 8+ 8 \times 9+ 9 \times 11)\\A=2( 88+ 72+99)\\A=2(259)\\A=518[/tex]
Therefore, the total surface area of the box is [tex]\fbox{\begin{minispace}\\518\text{ square inch}\end{minispace}}[/tex].
Since the price of contact paper is [tex]\$ \text{ }0.08 \text{ per square inch}[/tex] then the total cost of covering the box with contact paper is calculated as,
[tex]\fbox{\begin{minispace}\\\text{Total cost of contact paper in dollars}=518\times 0.08\\=41.44\end{minispace}}[/tex]
Hence, Erin needs to spend [tex]\fbox{\begin{minispace}\\\$\text{ }41.44\\\end{minispace}}[/tex] to cover the rectangular prism box completely with the contact paper.
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Answer details
Grade: High school
Subject: Mathematics
Chapter: Linear equation
Keywords: contact paper, box, rectangular prsim, prism box, 8 cents, 11 inches, 9 inches, 8 inches, length, breadth, height, surface area, Erin, spend, square inch, total surface area.
