the diameter of a sphere is 4 centimeters. which represents the volume of the sphere?

$\bigcirc$ $\frac{32}{3}\pi\text{ cm}^3$
$\bigcirc$ $8\pi\text{ cm}^3$
$\bigcirc$ $\frac{64}{3}\pi\text{ cm}^3$
$\bigcirc$ $16\pi\text{ cm}^3$

Question

the diameter of a sphere is 4 centimeters. which represents the volume of the sphere?

$\bigcirc$ $\frac{32}{3}\pi\text{ cm}^3$
$\bigcirc$ $8\pi\text{ cm}^3$
$\bigcirc$ $\frac{64}{3}\pi\text{ cm}^3$
$\bigcirc$ $16\pi\text{ cm}^3$

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" ] } ## Find the radius of the sphere Using the *Volume of a Sphere* knowledge point $$ \begin{aligned} &d = 4\text{ cm}\ &r = \frac{d}{2} = \frac{4}{2} = 2\text{ cm} \end{aligned} $$ ## Calculate the volume of the sphere Using the *Volume of a Sphere* knowledge point $$ \begin{aligned} &V = \frac{4}{3}\pi r^3\ &V = \frac{4}{3}\pi (2)^3 = \frac{4}{3}\pi (8) = \frac{32}{3}\pi\text{ cm}^3 \end{aligned} $$

(A) $\frac{32}{3}\pi\text{ cm}^3$

(B) $8\pi\text{ cm}^3$

(C) $\frac{64}{3}\pi\text{ cm}^3$

(D) $16\pi\text{ cm}^3$

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

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Question

Explanation:

Find the radius of the sphere

Calculate the volume of the sphere

Answer: