find the area of the smaller sector. round to the nearest tenth.
area = ? \text{ ft}^2

Question

find the area of the smaller sector. round to the nearest tenth.
area =  ?  \text{ ft}^2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Sector Area Formula" ], "new_concepts": [], "current_concepts": [ "Sector Area Formula" ] } ## Identify the given values Using the *Sector Area Formula* knowledge point $$ \begin{aligned} &r = 7.13\text{ ft}\ &\theta = 50^\circ \end{aligned} $$ ## Calculate the area of the smaller sector Using the *Sector Area Formula* knowledge point $$ \begin{aligned} &\text{Area} = \frac{\theta}{360^\circ} \cdot \pi r^2\ &\text{Area} = \frac{50}{360} \cdot \pi \cdot (7.13)^2\ &\text{Area} = \frac{5}{36} \cdot \pi \cdot 50.8369\ &\text{Area} \approx 0.13889 \cdot 3.14159265 \cdot 50.8369\ &\text{Area} \approx 22.182\text{ ft}^2 \end{aligned} $$ ## Round to the nearest tenth Using the *Sector Area Formula* knowledge point $$ \text{Area} \approx 22.2\text{ ft}^2 $$ Find the area of the smaller sector. Round to the nearest tenth. Area = 22.2 $ft^2$ { "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

Calculate the area of the smaller sector

Round to the nearest tenth

Answer: