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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Area of a Sector", "Radian Measure" ], "current_concepts": [ "Area of a Sector", "Radian Measure" ] } ## Identify given values and formula $$ \begin{aligned} &\theta = \frac{\pi}{2} \text{ radians}\ &r = 6 \text{ units}\ &A = \frac{1}{2} r^2 \theta \end{aligned} $$ ## Calculate the area of the shaded sector $$ \begin{aligned} &A = \frac{1}{2} \cdot 6^2 \cdot \frac{\pi}{2}\ &A = \frac{1}{2} \cdot 36 \cdot \frac{\pi}{2}\ &A = 18 \cdot \frac{\pi}{2}\ &A = 9\pi \text{ units}^2 \end{aligned} $$

(A) $6\pi\text{ units}^2$

(B) $9\pi\text{ units}^2$

(C) $18\pi\text{ units}^2$

(D) $36\pi\text{ units}^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Area of a Sector" ] }

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Explanation:

Identify given values and formula

Calculate the area of the shaded sector

Answer: