A distribution pipe is 1.93 mi long. What is the volume of water in gallons if the pipe is 2.00 ft in diameter for a length of 1.46 mi and 18.0 in for the remainder?

• A. 150,000 gal
• B. 400,000 gal
• C. 213,840 gal
• D. 300,000 gal

Answer: (C)

When a pipe changes diameter along its length, treat the total volume as the sum of two cylinders: one for each diameter-length portion, using V = πr^2L.

Convert lengths and diameters to consistent units. The first segment is 1.46 miles with a diameter of 2.00 ft, and the remainder is 0.47 miles with a diameter of 18.0 inches (1.50 ft). Convert miles to feet: 1 mile = 5,280 ft, so L1 = 1.46 × 5,280 = 7,708.8 ft and L2 = 0.47 × 5,280 = 2,481.6 ft. Radii: r1 = 1.00 ft (D = 2.00 ft) and r2 = 0.75 ft (D = 1.50 ft).

Compute volumes:

V1 = π × (1.00)^2 × 7,708.8 ≈ 24,218 ft^3.

V2 = π × (0.75)^2 × 2,481.6 = π × 0.5625 × 2,481.6 ≈ 4,385 ft^3.

Total volume ≈ 24,218 + 4,385 = 28,603 ft^3.

Convert to gallons using 1 ft^3 ≈ 7.48052 gal:

28,603 × 7.48052 ≈ 213,840 gallons.

So the volume is about 213,840 gallons.