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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 : l h V = w .
Simplify to find the width: w = l h V .
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. Our goal is to rewrite this formula to solve for the width, w , when we know the values of V , l , and h .
Isolating the Width To isolate w , we need to divide both sides of the equation V = lw h by l h . This will give us an expression for w in terms of V , l , and h .
Solving for Width Dividing both sides of V = lw h by l h , we get: l h V = l h lw h Simplifying the right side of the equation, we have: l h V = w Thus, we can rewrite this as: w = l h V
Final Answer The formula to find the width of the base of the prism when the volume, length, and height are known is: w = l h V
Examples
Imagine you're designing a storage box for your room. You know the volume you need the box to hold and the length and height that will fit well in your space. By rearranging the volume formula, you can easily calculate the required width of the box to meet your needs. This kind of problem is also useful in construction, where you might need to determine the dimensions of a room or container based on a desired volume and other known dimensions. Understanding how to manipulate formulas helps in many practical situations where space and volume are important considerations.
To find the width of a rectangular prism when the volume, length, and height are known, use the formula w = l h V . Simply plug in the values for volume, length, and height to calculate the width. For example, if the volume is 120 cubic units, length is 10 units, and height is 3 units, the width will be 4 units.
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