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Chapter 2: Problem 17

Solve each formula for the specified variable. \(V=\pi r^{2} h\) for \(h\)

Short Answer

Expert verified
Isolate \( h \) to get \( h = \frac{V}{\pi r^{2}} \).

Step by step solution

01

Identify the Given Formula

The formula given is: \[V = \pi r^{2} h \] The task is to solve for the variable \( h \).
02

Isolate the Variable \( h \)

To isolate \( h \), divide both sides of the equation by \( \pi r^{2} \) to get: \[ \frac{V}{\pi r^{2}} = \frac{\pi r^{2} h}{\pi r^{2}} \] This simplifies to: \[ \frac{V}{\pi r^{2}} = h \]
03

Write the Isolated Variable

Now, the formula solved for \( h \) is: \[ h = \frac{V}{\pi r^{2}} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. These symbols represent numbers and operations that can be performed with them. When working with algebra, you'll often see variables like x, y, and z, which stand in for unknown values. Solving algebraic equations involves finding the values for these variables that make the equation true. For example, in the given equation V = , we're tasked with solving for the variable h. Understanding algebra is essential because it's the foundation for most higher-level math courses and many scientific disciplines.
formula manipulation
Manipulating formulas is a key skill in algebra. It involves rearranging equations to solve for a particular variable. Here, we start with the formula: V = . To solve for h specifically, we need to isolate it on one side. This process often includes:
  • Adding, subtracting, multiplying, or dividing both sides of the equation by the same number or expression
  • Using inverse operations to cancel out terms (like using division to cancel multiplication)
In this case, we divided both sides by to isolate h. The goal is to make h the subject of the equation.
solving for a variable
Solving for a variable means finding the value of that variable in a given equation. This often involves moving other terms to the opposite side of the equation. Here's a step-by-step breakdown: Step 1: Identify the given formula: V = Step 2: Divide both sides by to isolate the variable h: . This simplifies to: Step 3: Write the isolated variable: h = . At this point, the formula is rearranged, making h the subject. This method applies to any formula or equation. The steps are universally useful, regardless of the specific problem. It鈥檚 crucial to practice these steps to become comfortable solving for any variable.

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