Question

the volume of this rectangular prism is 257,664 cubic millimeters. what is the value of v? 96 mm 44 mm v = millimeters

Explanation:

Step1: Recall the volume formula

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, \(l = 96\) mm, \(w = 44\) mm, \(h=v\), and \(V = 257664\) \(mm^{3}\). So, \(257664=96\times44\times v\).

Step2: Calculate \(96\times44\)

\(96\times44=(100 - 4)\times44=100\times44-4\times44=4400 - 176 = 4224\). The equation becomes \(257664 = 4224\times v\).

Step3: Solve for \(v\)

Using the formula \(v=\frac{V}{l\times w}\), substitute \(V = 257664\) and \(l\times w=4224\). So, \(v=\frac{257664}{4224}\).
\(257664\div4224 = 61\).

Answer:

\(61\)