find the area of the smaller sector.

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

round your answer to the nearest hundredth.

Question

find the area of the smaller sector.

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

round your answer to the nearest hundredth.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Sector Area Formula" ], "current_concepts": [ "Sector Area Formula" ] } ## Identify the given parameters $$ \begin{aligned} r &= 8\text{ m} \ \theta &= 140^\circ \end{aligned} $$ ## Apply the sector area formula $$ \begin{aligned} \text{Area} &= \frac{\theta}{360^\circ} \cdot \pi r^2 \ \text{Area} &= \frac{140}{360} \cdot \pi \cdot 8^2 \ \text{Area} &= \frac{7}{18} \cdot 64\pi \ \text{Area} &= \frac{224\pi}{9} \end{aligned} $$ ## Calculate and round the final value $$ \begin{aligned} \text{Area} &\approx \frac{224 \cdot 3.14159265}{9} \ \text{Area} &\approx 78.19079 \ \text{Area} &\approx 78.19\text{ m}^2 \end{aligned} $$ Find the area of the smaller sector. Area = 78.19 $\text{m}^2$ Round your answer to the nearest hundredth. { "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 parameters

Apply the sector area formula

Calculate and round the final value

Answer: