the volume of a cylinder is $156\pi\text{ cm}^3$. what is the volume of a cone with the same base and height as the cylinder?

$\bigcirc$ $39\pi\text{ cm}^3$
$\bigcirc$ $52\pi\text{ cm}^3$
$\bigcirc$ $78\pi\text{ cm}^3$
$\bigcirc$ $156\pi\text{ cm}^3$

Question

the volume of a cylinder is $156\pi\text{ cm}^3$. what is the volume of a cone with the same base and height as the cylinder?

$\bigcirc$ $39\pi\text{ cm}^3$
$\bigcirc$ $52\pi\text{ cm}^3$
$\bigcirc$ $78\pi\text{ cm}^3$
$\bigcirc$ $156\pi\text{ cm}^3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Volume Relationship between Cylinder and Cone" ], "new_concepts": [], "current_concepts": [ "Volume Relationship between Cylinder and Cone" ] } ## Identify the volume relationship $$ V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}} $$ ## Calculate the volume of the cone $$ V_{\text{cone}} = \frac{1}{3} \times 156\pi = 52\pi\text{ cm}^3 $$

(A) $39\pi\text{ cm}^3$

(B) $52\pi\text{ cm}^3$

(C) $78\pi\text{ cm}^3$

(D) $156\pi\text{ cm}^3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Volume Relationship between Cylinder and Cone" ] }

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Question

Explanation:

Identify the volume relationship

Calculate the volume of the cone

Answer: