Problem 14 - Algebra for College Students

Question

Solve each formula for the specified variable. \(V=\pi r^{2} h\) for \(h\) (volume of a right circular cylinder)

Step-by-Step Solution

Answer

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

Step 1: Identify the Formula

The given formula is for the volume of a right circular cylinder: \( V = \pi r^{2} h \)We need to solve this formula for the variable \( h \).

Step 2: Isolate the Variable

In order to solve for \( h \), we need to isolate it on one side of the equation. To do this, divide both sides of the equation by \( \pi r^{2} \):\[ \frac{V}{\pi r^{2}} = \frac{\pi r^{2} h}{\pi r^{2}} \]This simplifies to:\[ \frac{V}{\pi r^{2}} = h \]

Step 3: Rewrite the Equation

Rewrite the equation with \( h \) isolated on the left side:\( h = \frac{V}{\pi r^{2}} \)This is the formula solved for \( h \).

Key Concepts

volume of cylinder

In this exercise, we are working with the formula that calculates the volume of a cylinder. A cylinder is a three-dimensional shape with two parallel circular bases and a curved surface connecting them.
The essential formula for the volume of a cylinder is given by: \( V = \pi r^{2}h \).
Let's break this formula down:

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