find the length of arc abc.
use 3.14 for the value of $\pi$.

? cm
round to the nearest hundredth of a cm.

Question

find the length of arc abc.
use 3.14 for the value of $\pi$.

? cm
round to the nearest hundredth of a cm.

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": [ "Arc Length Formula", "Central Angle Theorem" ], "current_concepts": [ "Arc Length Formula", "Central Angle Theorem" ] } ## Identify the given values $$ \begin{aligned} r &= 54\text{ cm} \ \theta &= 240^\circ \ \pi &\approx 3.14 \end{aligned} $$ ## Apply the arc length formula $$ \begin{aligned} s &= \frac{\theta}{360^\circ} \cdot 2\pi r \ s &= \frac{240}{360} \cdot 2 \cdot 3.14 \cdot 54 \end{aligned} $$ ## Calculate the final value $$ \begin{aligned} s &= \frac{2}{3} \cdot 108 \cdot 3.14 \ s &= 72 \cdot 3.14 \ s &= 226.08\text{ cm} \end{aligned} $$ Find the length of arc ABC. Use 3.14 for the value of $\pi$. 226.08 cm Round to the nearest hundredth of a cm. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Arc Length Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Apply the arc length formula

Calculate the final value

Answer: