What is the volume of a pipe with an inside diameter of 2 inches and a length of 14 feet?

To find the volume of a pipe, the formula used is based on the volume of a cylinder, which is given by the equation ( V = \pi r^2 h ), where ( V ) is the volume, ( r ) is the radius of the pipe, and ( h ) is the height or length of the pipe.

First, we need to convert the dimensions of the pipe into consistent units. The inside diameter of the pipe is 2 inches, so the radius is half of that, which is 1 inch. Since the volume must ultimately be calculated in cubic feet, we will convert inches to feet. There are 12 inches in a foot, so the radius in feet is:

[

r = \frac{1 \text{ inch}}{12} = \frac{1}{12} \text{ feet}

]

The length of the pipe is provided as 14 feet.

Now we can plug these values into the volume formula. First, we calculate the area of the circular cross-section of the pipe:

[

\text{Area} = \pi r^2 = \pi \left( \frac{1}{12} \right)^2 = \pi \left(