If a lead pipe 1/4in.thick has an inner diameter of 1/2in.,find the number of cubic inches of lead in a pipe 10ft.long

If you tried using a typical 1/2 to 3/8 faucet connector such as https://www.homedepot.com/p/3-8-in-Compression-x-1-2-in-FIP-x-20-in-Braided-Polymer-Faucet-Connector-B1-20A-F/100459572, and it didn't work then ignore this answer, else...

Plumbing pipe size can be misleading due to the fact the pipe diameter is based on outer diameter and the inner diameter varies with wall thickness. To determine standard pipe diameter you measure the outer diameter and subtract 1/8".

The typical 1/2 inch pipe has an outer diameter of 5/8" and like wise a a 1/4" inner diameter pipe is a 3/8". So likely the typical faucet connector is correct. But you may have something unusual so FYI.

You can convert pipe size to gallons per minute of flow by calculating the cross-sectional area of the pipe and making some reasonable assumptions about pipe volume and the rate of flow. Pipe sizing is measured by the internal diameter of the pipe, not the overall outside diameter. Once determined, the overall volume can be calculated. Pipe flow is described in gallons per minute. Shorter lengths of pipe will have a greater flow than a longer length of the same diameter. This is caused by internal resistance of the pipe itself. By the same reasoning a larger diameter pipe will have a greater flow or GPM than a smaller pipe at the same pressure or flow rate. Pressure is described as pounds per square inch. The square-inch measurement is determined by the area of the pipe. The pounds are the amount of force that is placed on the liquid to push it through the enclosed space.With that background, you can estimate the flow based on the pipe size.
Find the cross-section area of the pipe. Area is equal to pi times the radius squared or a = 3.14 x r2. A two-inch diameter pipe would have a cross-section area of 3.14 x 12 or 3.14 square inches.
Understand that water has a certain pressure associated with the height of that water. One pound of water pressure, or 1 PSI, is equal to 2.31 feet of elevation in height. In other words, a 1-inch column or pipe of water that is 2.31 feet high will have a pressure of 1 PSI. The overall height -- not volume -- of the pipe corresponds to the pressure. A 6-inch diameter pipe that is 2.31 feet high will only have 1 PSI.
Find the volume of the 2-inch diameter pipe in Step 1 that has a length of 10 feet. Ten feet is equal to 120 inches. Multiply 3.14 square inches, the cross sectional area, times the length. The volume of the pipe is equal to 376.8 cubic inches of volume.
Convert cubic inches into cubic feet. One cubic foot equals 1,728 cubic inches. Divide 376.8 cubic inches by 1,728 cubic inches per cubic foot and the answer is .218 cubic feet. This means that the 2-inch diameter pipe that is 10 feet long has an internal volume of .218 cubic feet.
Calculate the amount of water that can be contained in the section of pipe at any given time. One cubic foot of water is equal to 7.48 gallons. Multiply 7.48 gallons by .218 cubic feet and the amount of water in the pipe is equal to 1.63 gallons.
Find the GPM if the flow of water is one foot per second. Multiply the one-foot per second flow by 60 seconds per minute and the flow is now 60 feet per minute. In other words the water will flow through the 10-foot pipe six full volumes for every minute. Since the piping contains 1.63 gallons per 10 feet of pipe, multiply 1.63 by six and the final GPM is equal to 9.78 GPM of water flow from the 2-inch diameter pipe.

Old method was to tap thick rope/cord in and around the pipe finish with a seal of silicone

0.23 gallons. Figured out by assuming the pipe is .75 inches inside diameter. To get the volume, calculate the area of the cross-section with the formula Pi times the radius squared. Which is 0.375 squared times Pi = 0.441786. Multiply that times 12 inches per foot times 10 feet = 53 cubic inches. One gallon = 231 cubic inches.

Just a little over 53.3 gallons

look up inside diameter of your 2' pipe
area inside a circle = 3.1415 (pi) x radius squared
for example if inside diameter of pipe is 1.75", then radius is half or .875
radius squared is .7656 x 3.1415 = 2.4 square inches

160 feet pipe = 1920 inches
2.4 square inches x 1920 = 4618 cubic inches

Then convert cubic inches into gallons:
http://www.metric-conversions.org/volume/cubic-inches-to-gallons.htm

If water is hot, then that can affect final calculation

Gene

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

at first calculate volume of outer tube i.e =4988.0313 cubic mm now inner volume of tube =2553.1968 cubic mm therefore total volume of aluminium =2434.8345 cubic mm now weight of the tube =2434.8345 x density of aluminium (gm/mm^3)

(1.5ft)^2 * Pi * 30 ft * 62.4 lbs/cu-ft = 13232.4 pounds plus the weight of the pipe which will vary depending on the material of the pipe.

You can find the weight of the pipe if you know the brand and material as most manufacturers will list the weight per foot in their catalog.
30 feet has about 11.94 cubic feet of whatever material the pipe is made of.

If the pipes are 3" outside diameter, the displacement is 24.15 cubic yards, however standard 3" pipe is 3.5" diameter, which would displace 32.85 cubic yards. 505.32 cubic yards is correct for the total trench volume.

3.14 x Diameter x Diameter / 4 x length= Volume in Cubic inches Diameter and Length are in inches.

Multiply the above volume by 0.004 to get gallons.