a formula for the volume of a sphere is $v = \frac{4}{3}\pi r^3$.

determine the volume of this sphere.

\begin{tabular}{|c|c|}
\hline
radius (units) & sphere volume (cubic units) \\
\hline
2 & \frac{32}{3}\pi \\
\hline
4 & \\
\hline
\end{tabular}

Question

a formula for the volume of a sphere is $v = \frac{4}{3}\pi r^3$.

determine the volume of this sphere.

\begin{tabular}{|c|c|}
\hline
radius (units) & sphere volume (cubic units) \\
\hline
2 & \frac{32}{3}\pi \\
\hline
4 & \\
\hline
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Volume of a Sphere" ], "current_concepts": [ "Volume of a Sphere" ] } ## Identify the given values and formula $$ \begin{aligned} &V = \frac{4}{3}\pi r^3\ &r = 4 \end{aligned} $$ ## Substitute the radius into the formula $$ \begin{aligned} &V = \frac{4}{3}\pi (4)^3 \end{aligned} $$ ## Calculate the final volume $$ \begin{aligned} &4^3 = 64\ &V = \frac{4}{3}\pi (64) = \frac{256}{3}\pi \end{aligned} $$ Determine the volume of this sphere. | Radius (units) | Sphere Volume (cubic units) | | :---: | :---: | | 2 | $\frac{32}{3}\pi$ | | 4 | $\frac{256}{3}\pi$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Volume of a Sphere" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Substitute the radius into the formula

Calculate the final volume

Answer: