Solve for w in the volume formula of a box:
v=lwh
The Correct Answer and Explanation is:
To solve for ( w ) in the volume formula of a box given by the equation ( V = lwh ), we need to isolate ( w ) on one side of the equation. Here, ( V ) represents the volume of the box, ( l ) is the length, ( w ) is the width, and ( h ) is the height of the box.
Step-by-Step Solution
- Start with the volume formula:
[
V = lwh
] - Isolate ( w ): To do this, divide both sides of the equation by ( lh ):
[
w = \frac{V}{lh}
]
Explanation
The formula ( V = lwh ) represents the relationship between the dimensions of a rectangular box and its volume. The volume ( V ) measures the space enclosed within the box and is expressed in cubic units (e.g., cubic centimeters, cubic meters). Each dimension—length ( l ), width ( w ), and height ( h )—is measured in linear units (e.g., centimeters, meters).
To find the width ( w ) when the volume and the other two dimensions are known, we rearrange the formula to isolate ( w ). This is a common practice in mathematics called “solving for a variable.” By dividing both sides of the equation by the product of the length and height (( lh )), we are effectively determining how wide the box must be to achieve a specific volume, given its length and height.
This formula is particularly useful in practical scenarios. For example, if you need to construct a box with a predetermined volume for shipping or storage, knowing the length and height can help you determine the necessary width. This can help optimize material usage and ensure the box fits into designated spaces, such as trucks or storage units.
In summary, by manipulating the volume formula ( V = lwh ), we derived the expression for width as ( w = \frac{V}{lh} ), allowing us to calculate the width of the box based on its volume and the other dimensions.