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Chapter 2: Problem 79

Solve each formula for the specified variable. \(V=L W H\) for \(H\)

Short Answer

Expert verified
H = \frac{V}{L W}

Step by step solution

01

- Understanding the formula

The given formula is for the volume of a rectangular prism: \( V = L W H \). Here, \( V \) is the volume, \( L \) is the length, \( W \) is the width, and \( H \) is the height. We need to solve the formula for \( H \).
02

- Isolate the variable

To isolate \( H \), we need to divide both sides of the equation by the product of \( L \) and \( W \): \[ V = L W H \] Therefore, divide both sides by \( L W \): \[ \frac{V}{L W} = \frac{L W H}{L W} \] This simplifies to: \[ \frac{V}{L W} = H \]
03

- Write the final solution

We have isolated \( H \) on one side of the equation. Thus, the formula solved for \( H \) is: \[ H = \frac{V}{L W} \]

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Key Concepts

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

algebraic manipulation
Algebraic manipulation involves performing operations on equations to solve for a specific variable. It includes actions like adding, subtracting, multiplying, dividing, and factoring both sides of the equation. These steps help simplify the equation or isolate the desired variable. Algebraic manipulation is essential in solving real-world problems by translating them into mathematical language.
isolating variables
Isolating a variable means getting the desired variable alone on one side of the equation. This process typically involves reversing the operations that have been applied to the variable. In the provided solution, we isolated the height (\(H\)) of a rectangular prism from the volume formula by dividing both sides of the equation by the product of length (\(L\)) and width (\(W\)). Starting from \(V = L W H\), we divided both sides by \(L W\) to get \(H = \frac{V}{L W}\).
Steps involved in isolating variables include:
  • Identify the operations affecting the variable by looking at the equation.
  • Reverse these operations step by step, maintaining the balance of the equation.
  • Simplify the equation after each step to keep it manageable and understandable.
rectangular prism volume formula
The formula for the volume of a rectangular prism, usually denoted by \(V = L W H\), shows how volume (\(V\)) is calculated based on the length (\(L\)), width (\(W\)), and height (\(H\)) of the prism. To understand the formula:
  • Volume is the amount of space enclosed within a 3D object.
  • Length is the measurement of the prism from one end to the other along its longest side.
  • Width is the distance across the prism, perpendicular to the length.
  • Height is the vertical distance from the base to the top of the prism.
When given the volume and the other dimensions, you can rearrange this formula to solve for any single dimension. In the example, we solved for \(H\) using \(H = \frac{V}{L W}\). This rearrangement allows us to find the height if we know the volume, length, and width.

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Most popular questions from this chapter

Solve each inequality. Graph the solution set, and write it using interval notation. \(9<-3 x<15\)

To see the connection between the solution of an equation and the solutions of the corresponding inequalities. Solve the following equation, and graph the solution set on a number line. \(3 x+2=14\)

If the sum of three consecutive odd integers is \(69,\) what is the third of the three odd integers?

If the first and third of three consecutive even integers are added, the result is 22 less than three times the second integer. Find the integers.

Graph the solution set, and write it using interval notation \(1 \leq 3+\frac{2}{3} p \leq 7\)
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