find the area of the shaded sector. round to the nearest hundredth.

$145^\circ$
$18\text{ ft}$
$\text{ft}^2$

Question

find the area of the shaded sector. round to the nearest hundredth.

$145^\circ$
$18\text{ ft}$
$\text{ft}^2$

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": [ "Area of Sector" ], "current_concepts": [ "Area of Sector" ] } ## Identify the given parameters $$ \begin{aligned} r &= 18\text{ ft} \ \theta &= 145^\circ \end{aligned} $$ ## Apply the sector area formula $$ \begin{aligned} A &= \frac{\theta}{360^\circ} \cdot \pi r^2 \ A &= \frac{145}{360} \cdot \pi \cdot 18^2 \ A &= \frac{29}{72} \cdot 324\pi \ A &= 130.5\pi \end{aligned} $$ ## Calculate the decimal value $$ \begin{aligned} A &\approx 130.5 \cdot 3.14159265 \ A &\approx 409.9778 \ A &\approx 409.98 \end{aligned} $$ Find the area of the shaded sector. Round to the nearest hundredth. 409.98 $ft^2$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of Sector" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Apply the sector area formula

Calculate the decimal value

Answer: