liliana is making a vase with a circular base. she wants the area of the base to be between $135\text{ cm}^2$ and $155\text{ cm}^2$.

which circle could represent the base of the vase?
use $3.14$ for $\pi$.

Question

liliana is making a vase with a circular base. she wants the area of the base to be between $135\text{ cm}^2$ and $155\text{ cm}^2$.

which circle could represent the base of the vase?
use $3.14$ for $\pi$.

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" ], "new_concepts": [], "current_concepts": [ "Area of a Circle" ] } ## Calculate the area for each radius option $$ \begin{aligned} &\text{For } r = 6\text{ cm}: A = 3.14 \times 6^2 = 3.14 \times 36 = 113.04\text{ cm}^2 \ &\text{For } r = 7\text{ cm}: A = 3.14 \times 7^2 = 3.14 \times 49 = 153.86\text{ cm}^2 \ &\text{For } r = 8\text{ cm}: A = 3.14 \times 8^2 = 3.14 \times 64 = 200.96\text{ cm}^2 \end{aligned} $$ ## Compare calculated areas with the target range $$ \begin{aligned} &135 < 153.86 < 155 \ &\text{The circle with radius } 7\text{ cm satisfies the condition.} \end{aligned} $$

Circle with radius 6 cm

Circle with radius 7 cm

Circle with radius 8 cm

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

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QUESTION IMAGE

Question

Explanation:

Calculate the area for each radius option

Compare calculated areas with the target range

Answer: