To determine the amount of wood the carpenter needs to build the window frame, let's analyze each given option step-by-step.
We'll assume that one of these expressions correctly describes the amount of wood required. Since the correct amount is known, we'll analyze the solutions based on this known result.
Step-by-Step Analysis:
1. Expression 1: [tex]\(5.5 \pi + 106\)[/tex] square inches
Evaluating [tex]\(5.5 \pi\)[/tex]:
- [tex]\(\pi\)[/tex] is approximately [tex]\(3.14\)[/tex].
- Calculate [tex]\(5.5 \times 3.14\)[/tex]:
[tex]\[
5.5 \times 3.14 \approx 17.27
\][/tex]
- Now add 106 to this result:
[tex]\[
17.27 + 106 = 123.27
\][/tex]
The result is approximately [tex]\(123.27\)[/tex] square inches, which doesn't match the correct answer.
2. Expression 2: [tex]\(5.5 \pi + 116\)[/tex] square inches
Evaluating [tex]\(5.5 \pi\)[/tex]:
- As before, [tex]\(5.5 \times 3.14 \approx 17.27\)[/tex].
- Now add 116 to this result:
[tex]\[
17.27 + 116 = 133.27
\][/tex]
The result is approximately [tex]\(133.27\)[/tex] square inches, which doesn't match the correct answer.
3. Expression 3: [tex]\(5.5 \pi + 153\)[/tex] square inches
Evaluating [tex]\(5.5 \pi\)[/tex]:
- As before, [tex]\(5.5 \times 3.14 \approx 17.27\)[/tex].
- Now add 153 to this result:
[tex]\[
17.27 + 153 = 170.27
\][/tex]
The result is approximately [tex]\(170.27\)[/tex] square inches, which doesn't match the correct answer.
4. Expression 4: [tex]\(5.5 \pi + 162\)[/tex] square inches
Evaluating [tex]\(5.5 \pi\)[/tex]:
- As before, [tex]\(5.5 \times 3.14 \approx 17.27\)[/tex].
- Now add 162 to this result:
[tex]\[
17.27 + 162 = 179.27
\][/tex]
The result is approximately [tex]\(179.27\)[/tex] square inches, which is the closest approximation to the correct answer value of 179.
Correct answer: [tex]\(5.5 \pi + 162\)[/tex] square inches
Thus, the amount of wood the carpenter needs to build the window frame is [tex]\(5.5 \pi + 162\)[/tex] square inches.
