9. jared wants a bird cage with a volume of at least 35 cubic feet for his parrot. the cage shown is on sale. is this bird cage large enough?
explain.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Volume of Prisms", "Unit Cube Counting" ], "new_concepts": [ "Composite Volume" ], "current_concepts": [ "Volume of Prisms", "Unit Cube Counting", "Composite Volume" ] } ## Identify the dimensions of the bird cage Using the *Unit Cube Counting* knowledge point $$ \begin{aligned} &\text{Length} = 4\text{ ft}\ &\text{Width} = 3\text{ ft}\ &\text{Height} = 3\text{ ft} \end{aligned} $$ ## Calculate the volume of the prism Using the *Volume of Prisms* knowledge point $$ \begin{aligned} V &= \text{length} \times \text{width} \times \text{height} \ V &= 4 \times 3 \times 3 \ V &= 36\text{ ft}^3 \end{aligned} $$ ## Compare with the required volume Compare the calculated volume to the minimum requirement. - Required: At least $35\text{ ft}^3$ - Actual: $36\text{ ft}^3$ - Since $36 \ge 35$, the cage is large enough. Yes, the bird cage is large enough. The volume of the rectangular prism cage is $36\text{ ft}^3$ (calculated as $4\text{ ft} \times 3\text{ ft} \times 3\text{ ft}$), which is greater than the required minimum of $35\text{ ft}^3$. { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Volume of Prisms" ] }

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Question

Explanation:

Identify the dimensions of the bird cage

Calculate the volume of the prism

Compare with the required volume

Answer: