\( V=\pi r^{2} h \quad \) for \( h \)

To solve the equation for height \( h \), you can rearrange the formula by dividing both sides by \( \pi r^{2} \). This gives you \( h = \frac{V}{\pi r^{2}} \). It's a nifty way to see how volume changes with height and radius, showing that for a fixed volume, increasing the radius will reduce the height required for that volume! When working with this formula, a common mistake is neglecting to ensure the units are consistent. If you have \( V \) in cubic centimeters and \( r \) in centimeters, make sure to use the same units throughout. Otherwise, you might end up with a height that doesn’t make sense, like asking for the height of a swimming pool with a radius of 1 meter but volume in milliliters—yikes!