determine (a) the area and (b) the circumference of the circle.

a. the area of the circle is 254.47 $\text{cm}^2$.
(type an integer or decimal rounded to the nearest hundredth as needed.)

Question

determine (a) the area and (b) the circumference of the circle.

a. the area of the circle is 254.47 $\text{cm}^2$.
(type an integer or decimal rounded to the nearest hundredth as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Area of Circle", "Circumference of Circle" ], "new_concepts": [], "current_concepts": [ "Area of Circle", "Circumference of Circle" ] } ## Identify the given radius Using the *Area of Circle* and *Circumference of Circle* knowledge points $$ r = 9\text{ cm} $$ ## Calculate the area of the circle Using the *Area of Circle* knowledge point $$ \begin{aligned} A &= \pi r^2 \ A &= \pi (9)^2 = 81\pi \ A &\approx 81 \times 3.14159265 \approx 254.469 \ A &\approx 254.47\text{ cm}^2 \end{aligned} $$ ## Calculate the circumference of the circle Using the *Circumference of Circle* knowledge point $$ \begin{aligned} C &= 2\pi r \ C &= 2\pi (9) = 18\pi \ C &\approx 18 \times 3.14159265 \approx 56.548 \ C &\approx 56.55\text{ cm} \end{aligned} $$ ## Question 1 a. The area of the circle is 254.47 $\text{cm}^2$. ## Question 2 b. The circumference of the circle is 56.55 $\text{cm}$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Area of Circle" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given radius

Calculate the area of the circle

Calculate the circumference of the circle

Answer:

Question 1

Question 2