Question

a furniture manufacturer is making a sofa with the dimensions shown. each sofa is filled with high - density foam that costs $0.02 per cubic inch. how much will each sofa cost to fill? $766.56 $933.12 $518.40 $414.72

Explanation:

Step1: Calculate the volume of the two parts

• Part 1:

The first part is a rectangular prism with length \(l = 72\) in, width \(w=10\) in, and height \(h = 36\) in.
The volume formula for a rectangular prism is \(V_1=l\times w\times h\).
So, \(V_1 = 72\times10\times36=25920\) cubic inches.

• Part 2:

The second part is a rectangular prism with length \(l = 72\) in, width \(w = 24\) in, and height \(h = 12\) in.
Using the volume formula \(V_2=l\times w\times h\), we get \(V_2=72\times24\times12 = 20736\) cubic inches.

Step2: Find the total volume

The total volume \(V = V_1+V_2\).
\(V=25920 + 20736=46656\) cubic inches.

Step3: Calculate the cost

The cost per cubic inch is \(\$0.02\).
The total cost \(C=V\times0.02\).
\(C = 46656\times0.02=\$933.12\)

Answer:

\(\$933.12\)