Determine the volume in gallons for the following distribution system: Distribution Pipe A: 489 ft in length, and 2.0 ft in diameter; Distribution Pipe B: 2,655 ft in the length and 1.5 ft in diameter; Storage Tank: 91 ft in diameter and a water height of 27.02 ft.

Determine the volume in gallons for the following distribution system: Distribution Pipe A: 489 ft in length, and 2.0 ft in diameter; Distribution Pipe B: 2,655 ft in the length and 1.5 ft in diameter; Storage Tank: 91 ft in diameter and a water height of 27.02 ft.

• A. 900,000 gallons
• B. 1,100,000 gallons
• C. 1,360,000 gallons
• D. 2,000,000 gallons

Answer: (C)

Volumes in a distribution system are found by treating each cylindrical element (pipes and storage tank) as a right circular cylinder and adding their volumes, then converting from cubic feet to gallons. For each pipe, use V = π (D/2)^2 × L. - Pipe A: D = 2.0 ft, L = 489 ft → V ≈ π × 1^2 × 489 ≈ 1,536 ft^3. - Pipe B: D = 1.5 ft, L = 2,655 ft → V ≈ π × (0.75)^2 × 2,655 ≈ π × 0.5625 × 2,655 ≈ 4,692 ft^3. Pipes total ≈ 6,228 ft^3. Tank volume uses the same formula with height as the fill depth: V = π r^2 h, r = D/2. - Tank: D = 91 ft ⇒ r = 45.5 ft, h = 27.02 ft → V ≈ π × (45.5)^2 × 27.02 ≈ π × 2070.25 × 27.02 ≈ π × 55,938.16 ≈ 175,735 ft^3. Total system volume ≈ 6,228 + 175,735 ≈ 181,963 ft^3. Convert to gallons: 1 ft^3 ≈ 7.48052 gallons, so total ≈ 181,963 × 7.48052 ≈ 1,361,000 gallons (about 1.36 million). The best match is about 1,360,000 gallons.

Volumes in a distribution system are found by treating each cylindrical element (pipes and storage tank) as a right circular cylinder and adding their volumes, then converting from cubic feet to gallons.

For each pipe, use V = π (D/2)^2 × L.

• Pipe A: D = 2.0 ft, L = 489 ft → V ≈ π × 1^2 × 489 ≈ 1,536 ft^3.

• Pipe B: D = 1.5 ft, L = 2,655 ft → V ≈ π × (0.75)^2 × 2,655 ≈ π × 0.5625 × 2,655 ≈ 4,692 ft^3.

Pipes total ≈ 6,228 ft^3.

Tank volume uses the same formula with height as the fill depth: V = π r^2 h, r = D/2.

• Tank: D = 91 ft ⇒ r = 45.5 ft, h = 27.02 ft → V ≈ π × (45.5)^2 × 27.02 ≈ π × 2070.25 × 27.02 ≈ π × 55,938.16 ≈ 175,735 ft^3.

Total system volume ≈ 6,228 + 175,735 ≈ 181,963 ft^3.

Convert to gallons: 1 ft^3 ≈ 7.48052 gallons, so total ≈ 181,963 × 7.48052 ≈ 1,361,000 gallons (about 1.36 million).

The best match is about 1,360,000 gallons.