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. 0.2 inches 4.5 inches 46.1 inches 414.7 inches

Explanation:

Step1: Rearrange the formula for width

We know the volume formula for a rectangular prism is \( V = lwh \). To solve for \( w \), we divide both sides of the formula by \( lh \), so we get \( w=\frac{V}{lh} \).

Step2: Substitute the given values

We are given that \( V = 138.24 \) cubic inches, \( l = 3.2 \) inches, and \( h = 9.6 \) inches. Substituting these values into the formula for \( w \), we have \( w=\frac{138.24}{3.2\times9.6} \).

Step3: Calculate the denominator

First, calculate the product of \( l \) and \( h \): \( 3.2\times9.6 = 30.72 \).

Step4: Calculate the width

Now, divide the volume by the product of length and height: \( w=\frac{138.24}{30.72}=4.5 \).

Answer:

B. 4.5 inches