To solve the equation $M = \pi r^2 h d$ for $r$, follow these steps:

Step 1: Isolate $r^2$

Start by dividing both sides of the equation by $\pi h d$ to get rid of the terms not involving $r$:

$r^2 = \frac{M}{\pi h d}$

Step 2: Solve for $r$

Take the square root of both sides to solve for $r$:

$r = \sqrt{\frac{M}{\pi h d}}$

Thus, the solution for $r$ is:

$r = \sqrt{\frac{M}{\pi h d}}$

Would you like more details on any of the steps or the reasoning behind them?

Here are five related questions to expand on this topic:

1. How do we determine when a denominator is not zero in an equation?
2. What is the significance of $\pi$ in equations involving circles or cylinders?
3. Can you explain the process of isolating variables in more complex equations?
4. How would the equation change if you were solving for $h$ instead of $r$?
5. What would happen if $h$ or $d$ were set to 0?

Tip: Always check for extraneous solutions, especially when square roots are involved.