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We are given the equation \( x = \frac{2}{3} \pi r^3 \) and are asked to solve for \( r \). Let's work through this step by step.

### Step 1: Isolate \( r^3 \)
We start with the equation:
\[
x = \frac{2}{3} \pi r^3
\]

Multiply both sides by \( \frac{3}{2\pi} \) to isolate \( r^3 \):
\[
r^3 = \frac{3x}{2\pi}
\]

### Step 2: Solve for \( r \)
Now, take the cube root of both sides to solve for \( r \):
\[
r = \sqrt[3]{\frac{3x}{2\pi}}
\]

### Conclusion
The correct expression for \( r \) is:
\[
r = \sqrt[3]{\frac{3x}{2\pi}}
\]

This matches **option B** in the given multiple-choice answers.

Do you need further details or have any questions?

### Related Questions:
1. How do you solve for a variable in terms of other variables in cubic equations?
2. What is the general method for solving equations involving powers like \( r^3 \)?
3. How do cube roots differ from square roots in terms of solving algebraic equations?
4. Can you provide a real-world example where solving for \( r \) like this might be useful?
5. What role does \( \pi \) play in volume-related equations like this?

### Tip:
Always isolate the variable of interest by performing inverse operations (e.g., multiplication, division, roots) step by step.

Learn how to solve the cubic equation x = (2/3)πr^3 for r using algebraic techniques. This solution involves isolating the variable and applying the cube root operation, suitable for students in Grades 10-12.

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