Question

the volume, v, of a rectangular prism is determined using the formula v=lwh, where l is the length, w is the width, and h is the height of the prism. using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches? round to the nearest tenth. \\(\circ\\) 0.2 inches \\(\circ\\) 4.5 inches \\(\circ\\) 46.1 inches \\(\circ\\) 414.7 inches

Explanation:

Step1: Rearrange the formula for width

Given \( V = lwh \), we solve for \( w \) by dividing both sides by \( lh \). So, \( w=\frac{V}{lh} \).

Step2: Substitute the given values

We know \( V = 138.24 \), \( l = 3.2 \), and \( h = 9.6 \). Substitute these into the formula: \( w=\frac{138.24}{3.2\times9.6} \).

Step3: Calculate the denominator

First, calculate \( 3.2\times9.6 = 30.72 \).

Step4: Calculate the width

Now, divide \( 138.24 \) by \( 30.72 \): \( w=\frac{138.24}{30.72}=4.5 \).

Answer:

4.5 inches (corresponding to the option: 4.5 inches)