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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Surface Area of a Sphere" ], "new_concepts": [], "current_concepts": [ "Surface Area of a Sphere", "Sphere Geometry" ] } ## Set up the surface area equation $$ \begin{aligned} A &= 4\pi r^2 \ 452.16 &= 4(3.14)r^2 \ 452.16 &= 12.56r^2 \end{aligned} $$ ## Solve for the radius $$ \begin{aligned} r^2 &= \frac{452.16}{12.56} \ r^2 &= 36 \ r &= 6\text{ in} \end{aligned} $$ ## Calculate the diameter $$ \begin{aligned} d &= 2r \ d &= 2(6) = 12\text{ in} \end{aligned} $$

(A) 6 in

(B) 12 in

(C) 24 in

(D) 36 in

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

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Question

Explanation:

Set up the surface area equation

Solve for the radius

Calculate the diameter

Answer: