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Chapter 2: Problem 74

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

Short Answer

Expert verified
W = \frac{V}{LH}

Step by step solution

01

Identify the Formula

The given formula is the volume of a rectangular prism: \(V = LWH\). We need to solve for \(W\).
02

Isolate the Desired Variable

We need to isolate \(W\). To do that, divide both sides of the equation by \(LH\): \[W = \frac{V}{LH}\]
03

Simplify the Expression

The expression is already simplified and isolated for \(W\). The final equation is: \[W = \frac{V}{LH}\]

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Key Concepts

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

Isolating Variables
In algebra, solving for a specific variable means isolating it on one side of the equation. This can involve moving other variables and constants to the opposite side. It's a foundational skill for solving equations.
To isolate a variable, you need to:
  • Identify the given equation and the variable you need to solve for.
  • Use algebraic operations, like addition, subtraction, multiplication, or division, to move other terms away from the desired variable.
For example, in our problem with the formula for the volume of a rectangular prism, we start with:
\[V = LWH\]
To solve for the width (\(W\)), we need to isolate it. We accomplish this by dividing both sides of the equation by the product of the length (\(L\)) and the height (\(H\)). This action effectively moves these terms to the opposite side of the equation, leaving \(W\) by itself.
Formula Manipulation
Formula manipulation involves rearranging equations to make it easier to solve for a particular variable. Often, you use properties of equality to move the terms around.
Key steps include:
  • Identifying the term you need to isolate.
  • Rearranging other terms by performing inverse operations (e.g., using division to counter multiplication).
In our problem, we start with the volume formula of a rectangular prism:
\[V = LWH\]
To isolate \(W\), the inverse of multiplication (\(L\) and \(H\)) is division. By dividing both sides of the equation by \(LH\), we get:
\[W = \frac{V}{LH}\]
Remember, whatever you do to one side of the equation, you must do to the other to maintain balance.
This principle ensures the equation stays valid while isolating the desired variable.
Volume of a Rectangular Prism
The volume of a rectangular prism is a measure of the space inside the prism. It's calculated using the formula:
\[V = LWH\]
Volume (\(V\)) is the product of length (\(L\)), width (\(W\)), and height (\(H\)). These three dimensions define the size and shape of the rectangular prism.
To find the volume, simply multiply these three measurements:
  • If \(L = 5\) cm, \(W = 3\) cm, and \(H = 2\) cm.
  • The volume (\(V\)) would be:
    \[V = 5 \times 3 \times 2 = 30\] cubic cm
This formula applies to any rectangular prism, regardless of its specific dimensions. It's essential for solving real-life problems involving space and capacity.

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