Final answer:
To solve the equation x = 4/3 πr³ for r, multiply both sides by 3/4, then divide by π, and finally take the cube root of both sides resulting in the solution r = ∛(3x/(4π)).
Step-by-step explanation:
The student is asking to solve the equation for r when given x = 4/3 πr³. To solve for r, we need to manipulate the equation to isolate r on one side. We can do this in the following steps:
- Multiply both sides of the equation by 3/4 to get rid of the fraction on the right side: 3/4 * x = πr³.
- Next, divide both sides by π to get r³ on its own: (3/4x)/π = r³.
- Finally, take the cube root of both sides to solve for r: r = ∛((3/4)x/π).
Therefore, the correct answer is:
r = ∛(3x/(4π))