FCTC Firefighter Math Applications Questions and Answers 3 — Questions and Answers
Question 1: A fire engine pump is supplying water at 150 psi engine pressure through 200 feet of 2.5-inch hose with a friction loss of 15 psi per 100 feet. What is the nozzle pressure?
- 90 psi
- 120 psi (Correct answer)
- 135 psi
- 150 psi
Correct answer: 120 psi
Friction loss = 15 psi × 2 (for 200 ft) = 30 psi; nozzle pressure = 150 − 30 = 120 psi.
Question 2: A storage tank is cylindrical with a diameter of 10 feet and a height of 8 feet. Approximately how many gallons does it hold? (1 cu ft ≈ 7.48 gal)
- 3,140 gallons
- 4,712 gallons (Correct answer)
- 4,208 gallons
- 6,280 gallons
Correct answer: 4,712 gallons
Volume = π × r² × h = 3.14 × 25 × 8 ≈ 628 cu ft; 628 × 7.48 ≈ 4,697 ≈ 4,712 gal.
Question 3: A hose line flows 200 gpm. How many minutes will it take to empty a 3,000-gallon tank?
- 10 minutes
- 12 minutes
- 15 minutes (Correct answer)
- 20 minutes
Correct answer: 15 minutes
Time = 3,000 ÷ 200 = 15 minutes.
Question 4: Friction loss in a 1.75-inch hose is 25 psi per 100 feet. A pumper must supply a nozzle pressure of 100 psi through 300 feet of hose. What pump discharge pressure is required?
- 125 psi
- 150 psi
- 175 psi (Correct answer)
- 200 psi
Correct answer: 175 psi
Friction loss = 25 × 3 = 75 psi; pump pressure = 100 + 75 = 175 psi.
Question 5: A ladder truck's aerial ladder is extended 85 feet at a 70° angle. Approximately how high does the tip reach vertically? (sin 70° ≈ 0.94)
- 59 feet
- 72 feet
- 80 feet (Correct answer)
- 84 feet
Correct answer: 80 feet
Vertical height = 85 × sin 70° = 85 × 0.94 ≈ 79.9 ≈ 80 feet.
Question 6: A room measures 20 ft × 15 ft × 9 ft. What is its volume in cubic feet?
- 1,800 cu ft
- 2,200 cu ft
- 2,700 cu ft (Correct answer)
- 3,000 cu ft
Correct answer: 2,700 cu ft
Volume = 20 × 15 × 9 = 2,700 cubic feet.
Question 7: If a pumper delivers 750 gpm and the hydrant can supply 1,200 gpm, how many additional gallons per minute are available from the hydrant beyond what the pumper uses?
- 350 gpm
- 400 gpm
- 450 gpm (Correct answer)
- 500 gpm
Correct answer: 450 gpm
Remaining supply = 1,200 − 750 = 450 gpm.
FCTC Firefighter Math Applications Questions and Answers 3
A fire engine pump is supplying water at 150 psi engine pressure through 200 feet of 2.5-inch hose with a friction loss of 15 psi per 100 feet.
What is the nozzle pressure?