directions
answer the questions below to check your understanding and move forward in the course! this quiz is not graded.

given a circumference of $89.4\text{ yd}$, what is the radius? use $3.14$ for $\pi$.

select the correct answer
- $56.9\text{ yd}$
- $561.4\text{ yd}$
- $14.2\text{ yd}$
- $28.5\text{ yd}$

Question

directions
answer the questions below to check your understanding and move forward in the course! this quiz is not graded.

given a circumference of $89.4\text{ yd}$, what is the radius? use $3.14$ for $\pi$.

select the correct answer
- $56.9\text{ yd}$
- $561.4\text{ yd}$
- $14.2\text{ yd}$
- $28.5\text{ yd}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circumference Formula Application" ], "new_concepts": [], "current_concepts": [ "Circumference of a Circle", "Diameter and Radius", "Circumference Formula Application" ] } ## State the circumference formula $$ C = 2\pi r $$ ## Substitute the given values $$ \begin{aligned} C &= 89.4 \ \pi &\approx 3.14 \ 89.4 &= 2 \cdot 3.14 \cdot r \ 89.4 &= 6.28 \cdot r \end{aligned} $$ ## Solve for the radius $$ \begin{aligned} r &= \frac{89.4}{6.28} \ r &\approx 14.2357 \text{ yd} \end{aligned} $$

(A) 56.9 yd

(B) 561.4 yd

(C) 14.2 yd

(D) 28.5 yd

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circumference Formula Application" ] }

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QUESTION IMAGE

Question

Explanation:

State the circumference formula

Substitute the given values

Solve for the radius

Answer: