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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
The formula for is:

Step by step solution

01

Write the Given Formula

Start with the given formula: . This is the formula for the volume of a rectangular prism.
02

Isolate the Desired Variable (W)

To solve for the variable , we need to isolate it on one side of the equation. Divide both sides of the equation by .
03

Simplify the Equation

After dividing both sides by , the equation becomes: .
04

Present the Solution

The final equation, with {sym} isolated, is:

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Key Concepts

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

isolating variables
In algebra, isolating a variable means rearranging an equation in order to get a specific variable by itself on one side of the equation. This helps us solve for that variable. For example, if we are given the formula for the volume of a rectangular prism, \( V = L \times W \times H \), and we need to solve for \( W \), we will isolate \( W \). Here are the steps to isolate \( W \):

  • Start with the equation \( V = L \times W \times H \).
  • To isolate \( W \), we need to get rid of \( L \) and \( H \) on the right side. We can do this by dividing both sides of the equation by \( L \times H \).
  • After dividing, the equation becomes \( \frac{V}{L \times H} = W \).

Now \( W \) is isolated, and we can see that \( W \) is equal to the volume divided by the product of the length and the height.
rectangular prism
A rectangular prism is a 3-dimensional shape with six faces, all of which are rectangles. It is called a prism because it has the same cross-section along a length. Rectangular prisms are very common in everyday life. Examples include boxes, bricks, and books.

The formula for the volume of a rectangular prism, \( V = L \times W \times H \), tells us how much space is inside the prism. Here,
  • \( L \) stands for the length,
  • \( W \) stands for the width, and
  • \( H \) stands for the height.
Each of these measurements needs to be in the same units for the formula to work properly. Understanding rectangular prisms helps in solving various real-life problems, such as figuring out how much a box can hold or how much material is needed to make it.
volume formula
The volume formula for a rectangular prism is \( V = L \times W \times H \). This formula calculates the space inside the prism by multiplying its length, width, and height. When solving problems using this formula:

  • Ensure all dimensions are in the same units before calculating.
  • Remember that the result will be in cubic units, such as cubic meters (m鲁) or cubic centimeters (cm鲁).
Using the volume formula is very straightforward:
  • Plug in the values for \( L \), \( W \), and \( H \)
  • Multiply them together to get the volume
For instance, if \( L = 5 m \), \( W = 3 m \), and \( H = 2 m \), then the volume \( V \) will be \( 5 \times 3 \times 2 = 30 \text{ } m^3 \). Understanding and using this formula is very important in fields like architecture, engineering, and everyday problem-solving.

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