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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": [ "Area of a Circle", "Area of a Rectangle" ], "new_concepts": [], "current_concepts": [ "Area of a Circle", "Area of a Rectangle" ] } ## Calculate the area of the bottom of the round pan $$ \begin{aligned} d &= 10\text{ in.} \ r &= 5\text{ in.} \ A_{\text{round}} &= \pi r^2 = \pi (5)^2 = 25\pi \approx 78.54\text{ sq in.} \end{aligned} $$ ## Calculate the area of the bottom of the rectangular pan $$ \begin{aligned} l &= 10\text{ in.} \ w &= 7\text{ in.} \ A_{\text{rect}} &= l \times w = 10 \times 7 = 70\text{ sq in.} \end{aligned} $$ ## Compare the two areas $$ \begin{aligned} A_{\text{round}} - A_{\text{rect}} &\approx 78.54 - 70 = 8.54\text{ sq in.} \ A_{\text{round}} &> A_{\text{rect}}\text{ by about } 8.5\text{ sq in.} \end{aligned} $$

(A) The area of the bottom of the round pan is greater than the area of the bottom of the rectangular pan by about 8.5 square inches.

(B) The area of the bottom of the round pan is greater than the area of the bottom of the rectangular pan by about 24.4 square inches.

(C) The area of the bottom of the round pan is less than the area of the bottom of the rectangular pan by about 7.2 square inches.

(D) The area of the bottom of the round pan is less than the area of the bottom of the rectangular pan by about 38.6 square inches.

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

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Question

Explanation:

Calculate the area of the bottom of the round pan

Calculate the area of the bottom of the rectangular pan

Compare the two areas

Answer: