If 300 feet of 12-inch pipe is uniformly coated with one inch of grease, how many gallons will it hold when filled with water?

To determine how many gallons of water a pipe holds when filled, we can start by calculating the total internal volume of the pipe with the grease coating factored in.

First, note the dimensions of the pipe: it's a 12-inch diameter pipe with a 1-inch coating of grease. The effective diameter of the inner pipe when filled with grease becomes 12 inches - 2 inches (1 inch on each side) = 10 inches.

Next, we need to calculate the volume of that inner section of the pipe. The formula for the volume ( V ) of a cylinder is:

[ V = \pi r^2 h ]

where ( r ) is the radius and ( h ) is the height (or length) of the cylinder.

1. The radius of the inner pipe with grease is ( 10 / 2 = 5 ) inches.
2. The height of the pipe is 300 feet. We need to convert this to inches: ( 300 \text{ feet} \times 12 \text{ inches/foot} = 3600 \text{ inches} ).

Now, we can plug these values into the formula:

[ V = \pi (