Question

topic: solids
progress:
question id: 1192752
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
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.
the solution is

Explanation:

Step1: Calculate volume of rectangular - bar

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

Step2: Calculate volume of cylinder

The volume of a cylinder is $V_{cyl}=\pi r^{2}h$. The diameter of the cylinder is $d = 2$ inches, so the radius $r=\frac{d}{2}=1$ inch, and the height $h = 16$ inches. Using $\pi = 3.14$, we have $V_{cyl}=3.14\times1^{2}\times16=50.24$ cubic - inches.

Step3: Calculate volume of composite solid

The volume of the composite solid $V = V_{rect}-V_{cyl}$. So $V=256 - 50.24=205.76$ cubic - inches.

Answer:

205.76