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

a. the area of the circle is 572.40 $\text{ft}^2$.
(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 572.40 $\text{ft}^2$.
(type an integer or decimal rounded to the nearest hundredth as needed.)

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Area of Circle" ], "new_concepts": [ "Circumference of Circle" ], "current_concepts": [ "Area of Circle", "Circumference of Circle" ] } ## Find the radius of the circle Using the *Area of Circle* knowledge point $$ \begin{aligned} &d = 27\text{ ft}\ &r = \frac{d}{2} = \frac{27}{2} = 13.5\text{ ft} \end{aligned} $$ ## Calculate the area of the circle Using the *Area of Circle* knowledge point $$ \begin{aligned} &A = \pi r^2 = \pi (13.5)^2 = 182.25\pi\text{ ft}^2\ &A \approx 182.25 \times 3.14159265 \approx 572.56\text{ ft}^2 \end{aligned} $$ ## Calculate the circumference of the circle We use the circumference formula: $$ C = \pi d $$ Substitute the given diameter: $$ C = 27\pi\text{ ft} $$ Calculate the decimal value: $$ C \approx 27 \times 3.14159265 \approx 84.82\text{ ft} $$ ## Question 1 The area of the circle is $572.56$ $\text{ft}^2$. ## Question 2 The circumference of the circle is $84.82$ $\text{ft}$. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Circumference of Circle" ] }

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QUESTION IMAGE

Question

Explanation:

Find the radius of the circle

Calculate the area of the circle

Calculate the circumference of the circle

Answer:

Question 1

Question 2