Solve the equation for the indicated variable. Assume no denominator is 0.

M = πr2hd, for r

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.

Solve the equation for the indicated variable. Assume no denominator is 0. M = πr^2hd, for r

Learn how to solve the equation M = πr^2hd for r, with a step-by-step solution. This problem covers algebraic and geometric concepts, including isolating variables and using square roots. Suitable for students in Grades 9-12.

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