Question

find the volume, in cubic inches, of the composite solid below, which consists of a 4 - inch square solid rectangular bar that is 16 inches in length. the bar has a 2 - inch diameter cylinder hole cut out of the center of the bar from the top of the bar through the entire length of the bar. use $\pi = 3.14$ to find the volume. enter only the number.

Explanation:

Step1: Calculate the volume of the rectangular bar

The volume of a rectangular prism is \(V = l\times w\times h\). Here, \(l = 16\) inches, \(w = 4\) inches, \(h = 4\) inches. So \(V_{rectangle}=16\times4\times4=256\) cubic inches.

Step2: Calculate the volume of the cylindrical hole

The volume of a cylinder is \(V=\pi r^{2}h\). Given \(d = 2\) inches (so \(r=\frac{d}{2}=1\) inch) and \(h = 16\) inches, \(\pi = 3.14\). Then \(V_{cylinder}=3.14\times1^{2}\times16 = 50.24\) cubic inches.

Step3: Calculate the volume of the composite solid

Subtract the volume of the cylinder from the volume of the rectangular bar. \(V = V_{rectangle}-V_{cylinder}\). So \(V=256 - 50.24=205.76\)

Answer:

205.76