the radius of the circle shown below is 8 centimeters. what is the approximate length of $\widehat{xy}$?

a. 16.1 cm
b. 8.0 cm
c. 64.2 cm
d. 50.3 cm

Question

the radius of the circle shown below is 8 centimeters. what is the approximate length of $\widehat{xy}$?

a. 16.1 cm
b. 8.0 cm
c. 64.2 cm
d. 50.3 cm

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Arc Length Formula" ], "new_concepts": [], "current_concepts": [ "Arc Length Formula", "Radius of Circle" ] } ## Identify the given values and formula $$ \begin{aligned} r &= 8\text{ cm} \ \theta &= 115^\circ \ s &= \frac{\theta}{360^\circ} \cdot 2\pi r \end{aligned} $$ ## Calculate the arc length $$ \begin{aligned} s &= \frac{115}{360} \cdot 2 \cdot \pi \cdot 8 \ s &= \frac{23}{72} \cdot 16\pi \ s &= \frac{46}{9}\pi \approx 5.111 \cdot 3.14159 \approx 16.06\text{ cm} \end{aligned} $$ ## Match with the closest option $$ s \approx 16.1\text{ cm} $$

A. 16.1 cm

B. 8.0 cm

C. 64.2 cm

D. 50.3 cm

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Arc Length Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Calculate the arc length

Match with the closest option

Answer: