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

Explanation:

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<reasoning>

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
\[

$$\begin{aligned} V &= \frac{4}{3}\pi (3)^3\\ V &= \frac{4}{3}\pi (27)\\ V &= 4\pi (9)\\ V &= 36\pi\text{ cubic inches} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(12\pi\) cubic inches</mcq-option>
<mcq-correct>(B) \(36\pi\) cubic inches</mcq-correct>
<mcq-option>(C) \(64\pi\) cubic inches</mcq-option>
<mcq-option>(D) \(81\pi\) cubic inches</mcq-option>
</answer>

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Answer:

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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
\[

$$\begin{aligned} V &= \frac{4}{3}\pi (3)^3\\ V &= \frac{4}{3}\pi (27)\\ V &= 4\pi (9)\\ V &= 36\pi\text{ cubic inches} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(12\pi\) cubic inches</mcq-option>
<mcq-correct>(B) \(36\pi\) cubic inches</mcq-correct>
<mcq-option>(C) \(64\pi\) cubic inches</mcq-option>
<mcq-option>(D) \(81\pi\) cubic inches</mcq-option>
</answer>

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