Which statement about the capacity of the 1¾ inch hose in gallons per 50-foot section is true?

Which statement about the capacity of the 1¾ inch hose in gallons per 50-foot section is true?

• A. 6.25 gallons
• B. 5.5 gallons
• C. 7.0 gallons
• D. 6.0 gallons

Answer: (A)

Think about the volume inside a hose as a circular tube being filled along a 50-foot length. Use the inner diameter to find the cross-sectional area, then multiply by the length, and convert to gallons. For a 1¾ inch hose, the radius is 0.875 inches. The area is πr^2 ≈ π × (0.875)^2 ≈ 2.405 square inches. The 50-foot length is 600 inches, so the volume = 2.405 × 600 ≈ 1443 cubic inches. Since 1 gallon = 231 cubic inches, the gallons per 50-foot section ≈ 1443 / 231 ≈ 6.24 gallons, which rounds to 6.25 gallons. So the capacity is about 6.25 gallons per 50-foot section. The other options would require a different volume (e.g., 1386 in^3 for about 6.0 gallons, 1617 in^3 for about 7.0 gallons), which don’t match the exact geometric calculation for this hose size and section length.

Think about the volume inside a hose as a circular tube being filled along a 50-foot length. Use the inner diameter to find the cross-sectional area, then multiply by the length, and convert to gallons.

For a 1¾ inch hose, the radius is 0.875 inches. The area is πr^2 ≈ π × (0.875)^2 ≈ 2.405 square inches. The 50-foot length is 600 inches, so the volume = 2.405 × 600 ≈ 1443 cubic inches. Since 1 gallon = 231 cubic inches, the gallons per 50-foot section ≈ 1443 / 231 ≈ 6.24 gallons, which rounds to 6.25 gallons.

So the capacity is about 6.25 gallons per 50-foot section. The other options would require a different volume (e.g., 1386 in^3 for about 6.0 gallons, 1617 in^3 for about 7.0 gallons), which don’t match the exact geometric calculation for this hose size and section length.