Sure, let's solve this problem step by step.
### Step 1: Understand the Problem Requirements
We are given:
- A conduit with a total area of [tex]\(2.04\)[/tex] square inches.
- The total area occupied by the wires is [tex]\(0.93\)[/tex] square inches.
- The maximum fill percentage allowed for the conduit is [tex]\(40\%\)[/tex].
We need to determine if the wires can fit within the maximum allowed area of the conduit.
### Step 2: Calculate the Maximum Allowed Fill Area
First, let's find the maximum area that can be occupied by the wires within the conduit. This is given by [tex]\(40\%\)[/tex] of the conduit’s total area.
[tex]\[ \text{Max Fill Area} = 2.04 \, \text{square inches} \times 0.40 \][/tex]
### Step 3: Compute the Maximum Fill Area
[tex]\[ \text{Max Fill Area} = 2.04 \times 0.40 \][/tex]
[tex]\[ \text{Max Fill Area} = 0.816 \, \text{square inches} \][/tex]
### Step 4: Compare the Wires' Area with the Maximum Fill Area
Now we compare the total area of the wires (0.93 square inches) with the maximum fill area (0.816 square inches).
If the wires' area is less than or equal to the maximum fill area, they will fit within the conduit. Otherwise, they won't.
[tex]\[ 0.93 \, \text{square inches} > 0.816 \, \text{square inches} \][/tex]
### Step 5: Conclusion
Since the area of the wires (0.93 square inches) is greater than the maximum allowable fill area (0.816 square inches), the wires cannot fit within the conduit under the given constraints.
Hence:
- Maximum Fill Area: [tex]\(0.816 \, \text{square inches}\)[/tex]
- Fit Status: The wires cannot fit within the conduit.
So, a 1 [tex]\( \frac{1}{2} \)[/tex]" conduit with a total area of 2.04 square inches cannot be filled with wires totaling 0.93 square inches if the maximum fill allowed is [tex]\(40\%\)[/tex].
