find the area of the larger sector.
round to the nearest tenth.

area = $ ? \text{ miles}^2 $

Question

find the area of the larger sector.
round to the nearest tenth.

area = $ ? \text{ miles}^2 $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Sector Area Formula" ], "new_concepts": [], "current_concepts": [ "Sector Area Formula" ] } ## Identify the given values $$ \begin{aligned} r &= 13.4\text{ miles} \ \theta &= 255^\circ \end{aligned} $$ ## Apply the sector area formula $$ \begin{aligned} \text{Area} &= \frac{\theta}{360^\circ} \cdot \pi r^2 \ \text{Area} &= \frac{255}{360} \cdot \pi \cdot (13.4)^2 \end{aligned} $$ ## Calculate the numerical value $$ \begin{aligned} \text{Area} &= \frac{17}{24} \cdot \pi \cdot 179.56 \ \text{Area} &\approx 0.708333 \cdot 3.14159265 \cdot 179.56 \ \text{Area} &\approx 399.598 \approx 399.6 \end{aligned} $$ Find the area of the larger sector. Round to the nearest tenth. Area = 399.6 $\text{miles}^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Sector Area Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Apply the sector area formula

Calculate the numerical value

Answer: