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\\)

Explanation:

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<reasoning>

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
\[

$$\begin{aligned} &V = \frac{4}{3}\pi r^3\\ &V = \frac{4}{3}\pi (2)^3 = \frac{4}{3}\pi (8) = \frac{32}{3}\pi\text{ cm}^3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{32}{3}\pi\text{ cm}^3\)</mcq-correct>
<mcq-option>(B) \(8\pi\text{ cm}^3\)</mcq-option>
<mcq-option>(C) \(\frac{64}{3}\pi\text{ cm}^3\)</mcq-option>
<mcq-option>(D) \(16\pi\text{ cm}^3\)</mcq-option>
</answer>

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Answer:

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<reasoning>

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
\[

$$\begin{aligned} &V = \frac{4}{3}\pi r^3\\ &V = \frac{4}{3}\pi (2)^3 = \frac{4}{3}\pi (8) = \frac{32}{3}\pi\text{ cm}^3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{32}{3}\pi\text{ cm}^3\)</mcq-correct>
<mcq-option>(B) \(8\pi\text{ cm}^3\)</mcq-option>
<mcq-option>(C) \(\frac{64}{3}\pi\text{ cm}^3\)</mcq-option>
<mcq-option>(D) \(16\pi\text{ cm}^3\)</mcq-option>
</answer>

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