find the area of the sector. write your answer using \pi\ with no spaces.
$a_{\text{sector}} = $ $\text{in}^2$

Question

find the area of the sector. write your answer using \pi\ with no spaces.
$a_{\text{sector}} = $   $\text{in}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Area of a Sector" ], "new_concepts": [], "current_concepts": [ "Area of a Sector" ] } ## Identify given values and formula $$ \begin{aligned} r &= 12\text{ in} \ \theta &= 75^\circ \ \text{Area} &= \frac{\theta}{360^\circ} \cdot \pi r^2 \end{aligned} $$ ## Calculate the sector area $$ \begin{aligned} \text{Area} &= \frac{75}{360} \cdot \pi \cdot 12^2 \ &= \frac{5}{24} \cdot 144\pi \ &= 5 \cdot 6\pi \ &= 30\pi \end{aligned} $$ Find the area of the sector. Write your answer using "pi" with no spaces. $A_{\text{sector}} =$ 30pi $\text{in}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of a Sector" ] }

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Identify given values and formula

Calculate the sector area

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