question 1 of 25

to the nearest square centimeter, what is the area of the shaded sector in the circle shown below?

a. $23\text{ cm}^2$
b. $151\text{ cm}^2$
c. $138\text{ cm}^2$
d. $12\text{ cm}^2$

Question

question 1 of 25

to the nearest square centimeter, what is the area of the shaded sector in the circle shown below?

a. $23\text{ cm}^2$
b. $151\text{ cm}^2$
c. $138\text{ cm}^2$
d. $12\text{ cm}^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circle Definition", "Radius of Circle" ], "new_concepts": [ "Area of Sector" ], "current_concepts": [ "Circle Definition", "Radius of Circle", "Area of Sector" ] } ## Identify the given values $$ \begin{aligned} r &= 12\text{ cm} \ \theta &= 110^\circ \end{aligned} $$ ## Apply the sector area formula $$ \begin{aligned} \text{Area} &= \frac{\theta}{360^\circ} \cdot \pi r^2 \ \text{Area} &= \frac{110}{360} \cdot \pi \cdot 12^2 \ \text{Area} &= \frac{11}{36} \cdot 144\pi \ \text{Area} &= 44\pi \end{aligned} $$ ## Calculate the numerical value $$ \begin{aligned} \text{Area} &\approx 44 \cdot 3.14159265 \ \text{Area} &\approx 138.23\text{ cm}^2 \ \text{Area} &\approx 138\text{ cm}^2 \end{aligned} $$

A. $23\text{ cm}^2$

B. $151\text{ cm}^2$

C. $138\text{ cm}^2$

D. $12\text{ cm}^2$

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

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Apply the sector area formula

Calculate the numerical value

Answer: