Question

the height of a cone is twice the radius of its base.

what expression represents the volume of the cone, in cubic units?

\\(\frac{2}{3}\pi x^3\\)
\\(\frac{4}{3}\pi x^2\\)
\\(2\pi x^3\\)
\\(4\pi x^3\\)

Explanation:

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<reasoning>

Identify the given dimensions

Using the Volume of a Cone knowledge point
\[

$$\begin{aligned} &\text{Radius of the base, } r = x \\ &\text{Height of the cone, } h = 2x \end{aligned}$$

\]

Apply the volume formula

Using the Volume of a Cone knowledge point
\[

$$\begin{aligned} V &= \frac{1}{3}\pi r^2 h \\ V &= \frac{1}{3}\pi (x)^2 (2x) \\ V &= \frac{2}{3}\pi x^3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{2}{3}\pi x^3\)</mcq-correct>
<mcq-option>(B) \(\frac{4}{3}\pi x^2\)</mcq-option>
<mcq-option>(C) \(2\pi x^3\)</mcq-option>
<mcq-option>(D) \(4\pi x^3\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given dimensions

Using the Volume of a Cone knowledge point
\[

$$\begin{aligned} &\text{Radius of the base, } r = x \\ &\text{Height of the cone, } h = 2x \end{aligned}$$

\]

Apply the volume formula

Using the Volume of a Cone knowledge point
\[

$$\begin{aligned} V &= \frac{1}{3}\pi r^2 h \\ V &= \frac{1}{3}\pi (x)^2 (2x) \\ V &= \frac{2}{3}\pi x^3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(\frac{2}{3}\pi x^3\)</mcq-correct>
<mcq-option>(B) \(\frac{4}{3}\pi x^2\)</mcq-option>
<mcq-option>(C) \(2\pi x^3\)</mcq-option>
<mcq-option>(D) \(4\pi x^3\)</mcq-option>
</answer>

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