Question

b. If carboard costs $0.05 per square inch, how much will it cost to make 600 boxes?

Answer 1

The Solution:

Given:

We are required to find the amount it will cost to make 600 of the above boxes if cardboard cost $0.05 per square inch.

Step 1:

Find the surface area of the box.

$Total\text{ surface area}=2(L_1\times W_1)+2(L_2\times W_2)+2(L_3\times W_3)$

In this case,

$\begin{gathered} L_1=8in. \\ W_1=12in. \\ \\ L_2=3\imaginaryI n \\ W_2=12\imaginaryI n \\ \\ L_3=3\imaginaryI n \\ W_3=8\imaginaryI n \end{gathered}$

Substituting these values in the formula, we get:

$TSA=2(8\times12)+2(3\times12)+2(3\times8)$$TSA=2(96+36+24)=2\times156=312\text{ }in.^2$

Step 2:

Find the cost of one box.

$\begin{gathered} 1in^2=\text{\ 0.05} \\ So, \\ 312in.^2=312\times0.05=\text{ \ 15.60} \end{gathered}$

Step 3:

Find the cost of 600 boxes.

$\begin{gathered} 1\text{ box}=\text{ \ }15.60 \\ So, \\ 600\text{ boxes}=600\times15.60=\text{\ 9360} \end{gathered}$

Therefore, the correct answer is $9360.