Problem 28 - Introductory Algebra for College Students

Question

Solve the formula for the volume of a circular cylinder for \(h\)

Step-by-Step Solution

Answer

The height of a cylinder can be calculated as \(h = \frac{V}{\pi r^2}\)

Step 1: Identify the formula

The formula for the volume of a cylinder is \(V = \pi r^2 h\). To solve for \(h\), we need to rearrange this formula to make \(h\) the subject.

Step 2: Isolate \(h\)

To isolate \(h\), we can divide both sides of the equation by \(\pi r^2\). Doing so gives us the formula \(h = \frac{V}{\pi r^2}\). We divide the both sides by \(\pi r^2\) because it's multiplied with \(h\) on the right side.

Step 3: Simplify the Equation

The equation \(h = \frac{V}{\pi r^2}\) is as simplified as possible. It tells us how to find the height 'h' if we know the volume 'V' and radius 'r' of the cylinder.