consider circle y with radius $3\text{ m}$ and central angle $xyz$ measuring $70^\circ$.

what is the approximate length of minor arc $xz$?
round to the nearest tenth of a meter.

$1.8\text{ meters}$
$3.7\text{ meters}$
$15.2\text{ meters}$
$18.8\text{ meters}$

Question

consider circle y with radius $3\text{ m}$ and central angle $xyz$ measuring $70^\circ$.

what is the approximate length of minor arc $xz$?
round to the nearest tenth of a meter.

$1.8\text{ meters}$
$3.7\text{ meters}$
$15.2\text{ meters}$
$18.8\text{ meters}$

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", "Circle Geometry" ] } ## Identify given values and formula $$ \begin{aligned} &r = 3\text{ m} \ &\theta = 70^\circ \ &s = \frac{\theta}{360^\circ} \cdot 2\pi r \end{aligned} $$ ## Calculate the arc length $$ \begin{aligned} &s = \frac{70}{360} \cdot 2 \cdot \pi \cdot 3 \ &s = \frac{7}{36} \cdot 6\pi = \frac{7\pi}{6} \ &s \approx \frac{7 \cdot 3.14159}{6} \approx 3.665\text{ m} \end{aligned} $$ ## Round to the nearest tenth $$ s \approx 3.7\text{ meters} $$

1.8 meters

3.7 meters

15.2 meters

18.8 meters

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

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QUESTION IMAGE

Question

Explanation:

Identify given values and formula

Calculate the arc length

Round to the nearest tenth

Answer: