the radius of a sphere is 3 inches. which represents the volume of the sphere?

$12\pi$ cubic inches
$36\pi$ cubic inches
$64\pi$ cubic inches
$81\pi$ cubic inches

Question

the radius of a sphere is 3 inches. which represents the volume of the sphere?

$12\pi$ cubic inches
$36\pi$ cubic inches
$64\pi$ cubic inches
$81\pi$ cubic inches

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Volume of a Sphere" ], "new_concepts": [], "current_concepts": [ "Volume of a Sphere" ] } ## Identify the given values and formula Using the *Volume of a Sphere* knowledge point $$ \begin{aligned} &r = 3\text{ inches}\ &V = \frac{4}{3}\pi r^3 \end{aligned} $$ ## Calculate the volume of the sphere Using the *Volume of a Sphere* knowledge point $$ \begin{aligned} V &= \frac{4}{3}\pi (3)^3\ V &= \frac{4}{3}\pi (27)\ V &= 4\pi (9)\ V &= 36\pi\text{ cubic inches} \end{aligned} $$

(A) $12\pi$ cubic inches

(B) $36\pi$ cubic inches

(C) $64\pi$ cubic inches

(D) $81\pi$ cubic inches

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

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QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Calculate the volume of the sphere

Answer: