What is the total volume of a pipe that is 1000 feet long with an 8 inch diameter?

To determine the total volume of a pipe that is 1000 feet long with an 8-inch diameter, one can use the formula for the volume of a cylinder, which is given by:

[ \text{Volume} = \pi r^2 h ]

In this formula, ( r ) represents the radius of the cylinder, and ( h ) is the height (or length in the case of the pipe). The diameter of the pipe is 8 inches, so the radius would be half of that, which is 4 inches. It's necessary to convert the dimensions into consistent units since the length of the pipe is given in feet and the radius in inches.

To convert the radius from inches to feet: [ 4 \text{ inches} = \frac{4}{12} \text{ feet} = \frac{1}{3} \text{ feet} ]

Now substitute the radius and height into the volume formula. First, calculate the area of the circular base:

[ \text{Area} = \pi \left(\frac{1}{3}\right)^2 = \pi \times \frac{1}{9} \text{ square feet} \approx 0.3491 \