The problem asks to solve the equation $3v = h^2(3r - h)$ for $r$, where $v$ and $h$ are real numbers.

1. Problem Description

The problem asks to solve the equation $3v = h^2(3r - h)$ for $r$, where $v$ and $h$ are real numbers.

2. Solution Steps

We want to isolate $r$ in the equation $3v = h^2(3r - h)$.

First, distribute $h^2$ on the right side of the equation:

$3v = 3h^2r - h^3$

Next, add $h^3$ to both sides of the equation:

$3v + h^3 = 3h^2r$

Finally, divide both sides by $3h^2$ to solve for $r$:

$r = \frac{3v + h^3}{3h^2}$

We can also write this as:

$r = \frac{3v}{3h^2} + \frac{h^3}{3h^2}$

$r = \frac{v}{h^2} + \frac{h}{3}$

3. Final Answer

$r = \frac{3v + h^3}{3h^2}$ or $r = \frac{v}{h^2} + \frac{h}{3}$