a circle has a diameter of 3 meters. which statement about the circumference and area is true?

a comparison of the area and circumference is not possible since the area cannot be determined.
the numerical value of the circumference and area are equal.
the numerical value of the circumference is greater than the numerical value of the area.
the numerical value of the circumference is less than the numerical value of the area.

Question

a circle has a diameter of 3 meters. which statement about the circumference and area is true?

a comparison of the area and circumference is not possible since the area cannot be determined.
the numerical value of the circumference and area are equal.
the numerical value of the circumference is greater than the numerical value of the area.
the numerical value of the circumference is less than the numerical value of the area.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Area of a Circle", "Circumference of a Circle" ], "new_concepts": [], "current_concepts": [ "Area of a Circle", "Circumference of a Circle" ] } ## Calculate the circumference of the circle $$ \begin{aligned} &d = 3 \ &C = \pi d = 3\pi \approx 9.42 \end{aligned} $$ ## Calculate the area of the circle $$ \begin{aligned} &r = \frac{d}{2} = 1.5 \ &A = \pi r^2 = \pi (1.5)^2 = 2.25\pi \approx 7.07 \end{aligned} $$ ## Compare the numerical values $$ \begin{aligned} &3\pi > 2.25\pi \ &C > A \end{aligned} $$

(A) A comparison of the area and circumference is not possible since the area cannot be determined.

(B) The numerical value of the circumference and area are equal.

(C) The numerical value of the circumference is greater than the numerical value of the area.

(D) The numerical value of the circumference is less than the numerical value of the area.

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

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QUESTION IMAGE

Question

Explanation:

Calculate the circumference of the circle

Calculate the area of the circle

Compare the numerical values

Answer: