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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Volume of Cones", "Volume of Cylinders" ], "new_concepts": [], "current_concepts": [ "Volume of Cones", "Volume of Cylinders" ] } ## Calculate the volume of the cone Using the *Volume of Cones* knowledge point $$ \begin{aligned} r_{\text{cone}} &= w = 2.5\text{ in} \ h_{\text{cone}} &= x = 5\text{ in} \ V_{\text{cone}} &= \frac{1}{3} \pi r_{\text{cone}}^2 h_{\text{cone}} \ V_{\text{cone}} &\approx \frac{1}{3} \cdot 3.14 \cdot (2.5)^2 \cdot 5 \ V_{\text{cone}} &\approx \frac{1}{3} \cdot 3.14 \cdot 6.25 \cdot 5 \ V_{\text{cone}} &\approx 32.708\text{ in}^3 \end{aligned} $$ ## Calculate the volume of the cylinder (cup) Using the *Volume of Cylinders* knowledge point $$ \begin{aligned} d_{\text{cup}} &= y = 5\text{ in} \implies r_{\text{cup}} = \frac{5}{2} = 2.5\text{ in} \ h_{\text{cup}} &= z = 3\text{ in} \ V_{\text{cup}} &= \pi r_{\text{cup}}^2 h_{\text{cup}} \ V_{\text{cup}} &\approx 3.14 \cdot (2.5)^2 \cdot 3 \ V_{\text{cup}} &\approx 3.14 \cdot 6.25 \cdot 3 \ V_{\text{cup}} &\approx 58.875\text{ in}^3 \end{aligned} $$ ## Compare the volumes Using the *Volume of Cylinders* and *Volume of Cones* knowledge points $$ \begin{aligned} \Delta V &= V_{\text{cup}} - V_{\text{cone}} \ \Delta V &\approx 58.875 - 32.708 \ \Delta V &\approx 26.167 \approx 26.2\text{ in}^3 \end{aligned} $$

(A) The cup holds $26.2\text{ in}^3$ more ice cream than the cone.

(B) The cone holds $26.2\text{ in}^3$ more ice cream than the cup.

(C) The cup holds $32.7\text{ in}^3$ more ice cream than the cone.

(D) The cone holds $32.7\text{ in}^3$ more ice cream than the cup.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Volume of Cones" ] }

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Question

Explanation:

Calculate the volume of the cone

Calculate the volume of the cylinder (cup)

Compare the volumes

Answer: