Question

has a circumference of \\(36\pi\text{ cm}\\).

what is the length of the radius, \\(r\\)?

• \\(6\text{ cm}\\)
• \\(18\text{ cm}\\)
• \\(36\text{ cm}\\)
• \\(72\text{ cm}\\)

Explanation:

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"concepts_used": [
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],
"new_concepts": [],
"current_concepts": [
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</pre_analysis>

<reasoning>

Set up the circumference equation

\[
C = 2\pi r
\]

Substitute the given circumference and solve for r

\[

$$\begin{aligned} 36\pi &= 2\pi r \\ r &= \frac{36\pi}{2\pi} \\ r &= 18 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 6 cm</mcq-option>
<mcq-correct>(B) 18 cm</mcq-correct>
<mcq-option>(C) 36 cm</mcq-option>
<mcq-option>(D) 72 cm</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Circumference Formula"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
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"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
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],
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"Circumference Formula"
],
"new_concepts": [],
"current_concepts": [
"Circumference Formula",
"Circle Geometry"
]
}
</pre_analysis>

<reasoning>

Set up the circumference equation

\[
C = 2\pi r
\]

Substitute the given circumference and solve for r

\[

$$\begin{aligned} 36\pi &= 2\pi r \\ r &= \frac{36\pi}{2\pi} \\ r &= 18 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 6 cm</mcq-option>
<mcq-correct>(B) 18 cm</mcq-correct>
<mcq-option>(C) 36 cm</mcq-option>
<mcq-option>(D) 72 cm</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Circumference Formula"
]
}
</post_analysis>