The volume of a rectangular prism is calculated using the formula V = lwh, where V is the volume of the prism, l and w are the length and width of the base of the prism, respectively, and h is the height of the prism. Rewrite the formula to find the width of the base of the prism if the volume, length of the base, and height of the prism are already known.
Answer (2)
Start with the volume formula: V = lw h .
Divide both sides by l h to isolate w .
Simplify the equation to find the width.
The formula for the width is: w = l h V .
Explanation
Understanding the Problem We are given the formula for the volume of a rectangular prism: V = lw h , where V is the volume, l is the length, w is the width, and h is the height. We need to rewrite this formula to solve for the width, w , when the volume V , length l , and height h are known.
Isolating the Width To isolate w , we need to divide both sides of the equation by l h . This will give us the formula for w in terms of V , l , and h .
Rewriting the Formula Starting with the formula: V = lw h Divide both sides by l h :
l h V = l h lw h l h V = w So, the formula for the width is: w = l h V
Final Answer The width w of the rectangular prism can be found by dividing the volume V by the product of the length l and the height h . The rewritten formula is: w = l h V
Examples
Imagine you're designing a storage box and know the desired volume and length and height. By rearranging the volume formula, you can easily calculate the required width. This ensures your box meets your specific storage needs. This principle applies to various real-world scenarios, such as optimizing shelf space, calculating dimensions for packaging, or determining the size of containers for shipping.
To find the width w of a rectangular prism when the volume V , length l , and height h are known, use the formula w = l h V . This formula isolates the width by dividing the volume by the product of the length and height. An example illustrates how to apply this formula to calculate the width of a box.
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