find the area of each circle. (use 3.14 for $\pi$.)

2)
image of a circle with a diameter of 53 yd

Question

find the area of each circle. (use 3.14 for $\pi$.)

2)
image of a circle with a diameter of 53 yd

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Circle Diameter and Radius", "Circle Area Calculation" ], "new_concepts": [], "current_concepts": [ "Circle Diameter and Radius", "Circle Area Calculation" ] } ## Find the radius of the first circle Using the *Circle Diameter and Radius* knowledge point $$ \begin{aligned} d_1 &= 20\text{ ft}\ r_1 &= \frac{d_1}{2} = \frac{20}{2} = 10\text{ ft} \end{aligned} $$ ## Calculate the area of the first circle Using the *Circle Area Calculation* knowledge point $$ \begin{aligned} A_1 &= \pi r_1^2\ A_1 &\approx 3.14 \times 10^2\ A_1 &\approx 3.14 \times 100 = 314\text{ ft}^2 \end{aligned} $$ ## Find the radius of the second circle Using the *Circle Diameter and Radius* knowledge point $$ \begin{aligned} d_2 &= 53\text{ yd}\ r_2 &= \frac{d_2}{2} = \frac{53}{2} = 26.5\text{ yd} \end{aligned} $$ ## Calculate the area of the second circle Using the *Circle Area Calculation* knowledge point $$ \begin{aligned} A_2 &= \pi r_2^2\ A_2 &\approx 3.14 \times 26.5^2\ A_2 &\approx 3.14 \times 702.25 = 2205.065\text{ yd}^2 \end{aligned} $$ ## Question 1 $314\text{ ft}^2$ ## Question 2 $2205.065\text{ yd}^2$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Circle Area Calculation" ] }

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QUESTION IMAGE

Question

Explanation:

Find the radius of the first circle

Calculate the area of the first circle

Find the radius of the second circle

Calculate the area of the second circle

Answer:

Question 1

Question 2