Problem 44 - Algebra and Trigonometry

Question

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? \(V=\pi r^{2} h\) for \(h\)

Step-by-Step Solution

Answer

The formula \(h = \frac{V}{\pi r^{2}}\) describes the height of a cylinder when the volume, radius, and value of \(\pi\) are known.

Step 1: Identify the formula.

The formula \(V=\pi r^{2} h\) represents the volume of a cylinder where \(V\) is the volume, \(r\) is the radius of the base, and \(h\) is the height of the cylinder.

Step 2: Isolate the variable 'h'.

To isolate \(h\), divide both sides of the equation by \(\pi r^{2}\). The equation then becomes \(h = \frac{V}{\pi r^{2}}\).

Step 3: Simplify equation.

No further simplification is required