The formula for the volume of a cylinder is [tex]$V=\pi r^2 h$[/tex]. Solve [tex]$V=\pi r^2 h$[/tex] for [tex]$h$[/tex], the height of the cylinder.
A. [tex]$h=\frac{\pi}{V r^2}$[/tex]
B. [tex]$h=\frac{\pi r^2}{V}$[/tex]
C. [tex]$h=\frac{\pi V}{r^2}$[/tex]
D. [tex]$h=\frac{V}{\pi r^2}$[/tex]
Answer (2)
Start with the formula for the volume of a cylinder: V = π r 2 h .
Divide both sides of the equation by π r 2 to isolate h : π r 2 V = π r 2 π r 2 h .
Simplify the equation to find h : h = π r 2 V .
The solution is h = π r 2 V .
Explanation
Understanding the Formula We are given the formula for the volume of a cylinder: $V =
\pi r^2 h$, where:
V is the volume,
r is the radius, and
h is the height.
Our goal is to isolate h on one side of the equation.
Isolating h To solve for h , we need to divide both sides of the equation by π r 2 :
π r 2 V = π r 2 π r 2 h
This simplifies to:
h = π r 2 V
Finding the Correct Option Comparing our result with the given options, we see that option D matches our solution:
h = π r 2 V
Final Answer Therefore, the correct answer is D.
Examples
Understanding how to rearrange formulas like the volume of a cylinder is useful in many real-world scenarios. For example, if you know the volume of a can and its radius, you can calculate its height. This is useful in manufacturing, engineering, and even in everyday tasks like determining how much liquid a container can hold. By rearranging the formula, we can easily find the height: h = π r 2 V .
To solve the volume formula for a cylinder V = π r 2 h for height h , divide both sides by π r 2 , resulting in h = π r 2 V . The correct answer is option D. This allows you to find the height of the cylinder if you know its volume and radius.
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