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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

  1. Identify the equation We start with the equation given in the problem, which is the formula for the volume of a cylinder:

$$ V = \pi r^2 h $$

  1. 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 $r$.

$$ h = \frac{V}{\pi r^2} $$

  1. 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.
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