the circumference of a circle is $32\pi$ in. what is the area of the circle? write your answer using \pi\ with no spaces.

$a_{\text{circle}} = $ $\text{in}^2$

Question

the circumference of a circle is $32\pi$ in. what is the area of the circle? write your answer using \pi\ with no spaces.

$a_{\text{circle}} = $   $\text{in}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circumference Formula", "Area of a Circle", "Circle Formulas Relationship" ], "new_concepts": [], "current_concepts": [ "Circumference Formula", "Area of a Circle", "Circle Formulas Relationship" ] } ## Find the radius from the circumference $$ \begin{aligned} C &= 2\pi r \ 32\pi &= 2\pi r \ r &= 16 \end{aligned} $$ ## Calculate the area of the circle $$ \begin{aligned} A &= \pi r^2 \ A &= \pi (16)^2 \ A &= 256\pi \end{aligned} $$ The circumference of a circle is $32\pi$ in. What is the area of the circle? Write your answer using "pi" with no spaces. $A_{\text{circle}} =$ 256pi $\text{in}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of a Circle" ] }

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Explanation:

Find the radius from the circumference

Calculate the area of the circle

Answer: