v = πr²h, solve for h
Understand the Problem
The question is asking how to solve the equation V = πr²h for the variable h. This involves isolating h on one side of the equation, which requires manipulating the equation accordingly.
Answer
$$ h = \frac{V}{\pi r^2} $$
Answer for screen readers
$$ h = \frac{V}{\pi r^2} $$
Steps to Solve
- Identify the equation We start with the equation given in the problem, which is the formula for the volume of a cylinder:
$$ V = \pi r^2 h $$
- Isolate h To isolate $h$, we need to divide both sides of the equation by $\pi r^2$. This will give us an expression for $h$ in terms of $V$ and $r$.
$$ h = \frac{V}{\pi r^2} $$
- Final expression for h Now we have successfully solved for $h$. The formula we derived shows how to calculate the height of a cylinder when its volume $V$ and radius $r$ are known.
$$ h = \frac{V}{\pi r^2} $$
More Information
The formula $h = \frac{V}{\pi r^2}$ allows us to find the height of a cylinder if we know its volume and the radius. This concept is widely used in geometry and engineering applications.
Tips
- Forgetting to divide by $\pi r^2$, resulting in an incorrect equation for $h$.
- Confusing which variable to isolate when manipulating formulas.