what is the area of the sector created by $\widehat{pq}$?

write your answer using \pi\ with no spaces.

$a_{\text{sector}} =$ $\text{units}^2$

Question

what is the area of the sector created by $\widehat{pq}$?

write your answer using \pi\ with no spaces.

$a_{\text{sector}} =$   $\text{units}^2$

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 the given values $$ \begin{aligned} r &= 18 \ \theta &= 150^\circ \end{aligned} $$ ## Apply the sector area formula $$ \begin{aligned} A_{\text{sector}} &= \frac{\theta}{360^\circ} \cdot \pi r^2 \ A_{\text{sector}} &= \frac{150}{360} \cdot \pi \cdot 18^2 \end{aligned} $$ ## Calculate the final area $$ \begin{aligned} A_{\text{sector}} &= \frac{5}{12} \cdot 324\pi \ A_{\text{sector}} &= 5 \cdot 27\pi \ A_{\text{sector}} &= 135\pi \end{aligned} $$ What is the area of the sector created by $\widehat{PQ}$? Write your answer using "pi" with no spaces. $A_{\text{sector}} =$ 135pi $\text{units}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of a Sector" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Apply the sector area formula

Calculate the final area

Answer: