what is the approximate area of the shaded sector in the circle shown below?

a. $7.33\text{ in}^2$
b. $51\text{ in}^2$
c. $3.67\text{ in}^2$
d. $205\text{ in}^2$

Question

what is the approximate area of the shaded sector in the circle shown below?

a. $7.33\text{ in}^2$
b. $51\text{ in}^2$
c. $3.67\text{ in}^2$
d. $205\text{ in}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Radius of a Circle", "Arc Measure", "Area of a Sector" ], "new_concepts": [], "current_concepts": [ "Radius of a Circle", "Arc Measure", "Area of a Sector" ] } ## Identify the given values Using the *Radius of a Circle* and *Arc Measure* knowledge points $$ \begin{aligned} &r = 14\text{ in}\ &\theta = 30^\circ \end{aligned} $$ ## Calculate the sector area Using the *Area of a Sector* knowledge point $$ \begin{aligned} A &= \frac{\theta}{360^\circ} \cdot \pi r^2\ A &= \frac{30^\circ}{360^\circ} \cdot \pi (14)^2\ A &= \frac{1}{12} \cdot 196\pi\ A &= \frac{49}{3}\pi \approx 51.31\text{ in}^2 \end{aligned} $$ ## Match with the closest option Using the *Area of a Sector* knowledge point $$ \begin{aligned} A \approx 51\text{ in}^2 \end{aligned} $$

A. $7.33\text{ in}^2$

B. $51\text{ in}^2$

C. $3.67\text{ in}^2$

D. $205\text{ in}^2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Area of a Sector" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Calculate the sector area

Match with the closest option

Answer: