Question

the volume of the sphere is \\(\frac{500}{3}\pi\\) cubic units.

what is the value of \\(x\\)?

4 units
5 units
8 units
10 units

Explanation:

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<reasoning>

Identify the given values and formula

We are given that the volume of the sphere is \(V = \frac{500}{3}\pi\) cubic units. The radius of the sphere is labeled as \(x\). The formula for the volume of a sphere is:
\[V = \frac{4}{3}\pi r^3\]

Set up the equation for x

Using the Literal Equations knowledge point
\[
\frac{4}{3}\pi x^3 = \frac{500}{3}\pi
\]

Solve for x

Using the Literal Equations knowledge point
\[

$$\begin{aligned} 4x^3 &= 500\\ x^3 &= 125\\ x &= 5 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>4 units</mcq-option>
<mcq-correct>5 units</mcq-correct>
<mcq-option>8 units</mcq-option>
<mcq-option>10 units</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given values and formula

We are given that the volume of the sphere is \(V = \frac{500}{3}\pi\) cubic units. The radius of the sphere is labeled as \(x\). The formula for the volume of a sphere is:
\[V = \frac{4}{3}\pi r^3\]

Set up the equation for x

Using the Literal Equations knowledge point
\[
\frac{4}{3}\pi x^3 = \frac{500}{3}\pi
\]

Solve for x

Using the Literal Equations knowledge point
\[

$$\begin{aligned} 4x^3 &= 500\\ x^3 &= 125\\ x &= 5 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>4 units</mcq-option>
<mcq-correct>5 units</mcq-correct>
<mcq-option>8 units</mcq-option>
<mcq-option>10 units</mcq-option>
</answer>

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