Question

question 11 of 23 - multiple choice

the walls of a house are finished with 1\ x 8\ lap siding. if each course has 6-7/8\
exposed to the weather and there are 33 courses from the bottom to the top, what
is the height of the sided wall?

a 226-7/8\
b 173-1/4\
c 226-5/8\
d 264\

Explanation:

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"needs_drawing": false,
"concepts_used": [
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<reasoning>

Identify the given values and target

Using the Lap Siding Calculation knowledge point, we identify:

• Exposed height per course: \(6\frac{7}{8}''\)
• Total number of courses: \(33\)
• Target: Total height of the sided wall

Calculate the total height

Using the Mixed Numbers Multiplication knowledge point
\[

$$\begin{aligned} \text{Total Height} &= 33 \times 6\frac{7}{8} \\ &= 33 \times \frac{55}{8} \\ &= \frac{1815}{8} \\ &= 226\frac{7}{8}'' \end{aligned}$$

\]

Analyze the common misconception for Option B

We analyze why a student might incorrectly calculate \(173\frac{1}{4}''\) (Option B):

• If a student mistakenly uses the overlap or incorrect dimensions, such as subtracting the exposure from the nominal width: \(8 - 6\frac{7}{8} = 1\frac{1}{8}''\) overlap.
• If they multiply the overlap by the number of courses: \(33 \times 1\frac{1}{8} = 33 \times \frac{9}{8} = \frac{297}{8} = 37\frac{1}{8}''\).
• If they subtract this total overlap from the maximum un-overlapped height of \(33 \times 8'' = 264''\) (Option D):

\[
264 - 37\frac{1}{8} = 226\frac{7}{8}'' \quad (\text{which is correct})
\]

• However, if they make an arithmetic error or use an incorrect exposure value like \(5\frac{1}{4}''\) instead:

\[
33 \times 5\frac{1}{4} = 33 \times \frac{21}{4} = \frac{693}{4} = 173\frac{1}{4}''
\]
This shows Option B results from using an incorrect exposure of \(5\frac{1}{4}''\) per course.
</reasoning>

<answer>
<mcq-correct>A) 226-7/8"</mcq-correct>
<mcq-option>B) 173-1/4"</mcq-option>
<mcq-option>C) 226-5/8"</mcq-option>
<mcq-option>D) 264"</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Lap Siding Calculation"
]
}
</post_analysis>

Answer:

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"multiple_choice_formatter",
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"needs_drawing": false,
"concepts_used": [
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</pre_analysis>

<reasoning>

Identify the given values and target

Using the Lap Siding Calculation knowledge point, we identify:

• Exposed height per course: \(6\frac{7}{8}''\)
• Total number of courses: \(33\)
• Target: Total height of the sided wall

Calculate the total height

Using the Mixed Numbers Multiplication knowledge point
\[

$$\begin{aligned} \text{Total Height} &= 33 \times 6\frac{7}{8} \\ &= 33 \times \frac{55}{8} \\ &= \frac{1815}{8} \\ &= 226\frac{7}{8}'' \end{aligned}$$

\]

Analyze the common misconception for Option B

We analyze why a student might incorrectly calculate \(173\frac{1}{4}''\) (Option B):

• If a student mistakenly uses the overlap or incorrect dimensions, such as subtracting the exposure from the nominal width: \(8 - 6\frac{7}{8} = 1\frac{1}{8}''\) overlap.
• If they multiply the overlap by the number of courses: \(33 \times 1\frac{1}{8} = 33 \times \frac{9}{8} = \frac{297}{8} = 37\frac{1}{8}''\).
• If they subtract this total overlap from the maximum un-overlapped height of \(33 \times 8'' = 264''\) (Option D):

\[
264 - 37\frac{1}{8} = 226\frac{7}{8}'' \quad (\text{which is correct})
\]

• However, if they make an arithmetic error or use an incorrect exposure value like \(5\frac{1}{4}''\) instead:

\[
33 \times 5\frac{1}{4} = 33 \times \frac{21}{4} = \frac{693}{4} = 173\frac{1}{4}''
\]
This shows Option B results from using an incorrect exposure of \(5\frac{1}{4}''\) per course.
</reasoning>

<answer>
<mcq-correct>A) 226-7/8"</mcq-correct>
<mcq-option>B) 173-1/4"</mcq-option>
<mcq-option>C) 226-5/8"</mcq-option>
<mcq-option>D) 264"</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Lap Siding Calculation"
]
}
</post_analysis>