FCTC Firefighter Math Applications Questions and Answers Flashcards

A firefighter earns $22.50 per hour. How much does she earn for a 24-hour shift?

Answer: $540.00

$22.50 × 24 hours = $540.00 for the full shift.

A circular water storage tank has a diameter of 20 feet. What is the approximate area of its base? (Use π ≈ 3.14)

Answer: 314 sq ft

Radius = 10 ft; Area = π × r² = 3.14 × 100 = 314 square feet.

A fire engine uses 6 gallons of fuel per hour while pumping. How much fuel is consumed during a 3.5-hour operation?

Answer: 21 gallons

6 gallons/hr × 3.5 hours = 21 gallons consumed.

A ladder is placed against a building with its base 8 feet from the wall. The ladder reaches 15 feet up the wall. What is the approximate length of the ladder?

Answer: 17 feet

Using the Pythagorean theorem: √(8² + 15²) = √(64 + 225) = √289 = 17 feet.

A building's floor area is 4,500 square feet and is divided into equal-sized rooms. If each room is 300 square feet, how many rooms are in the building?

Answer: 15 rooms

4,500 sq ft ÷ 300 sq ft per room = 15 rooms.

A 1¾-inch hose line has a friction loss of 15.5 psi per 100 feet. What is the friction loss for a 200-foot hose lay?

Answer: 31 psi

15.5 psi × 2 (for 200 ft) = 31 psi total friction loss.

An aerial ladder must reach a window 72 feet above ground. If the ladder is set at a 70° working angle, approximately what horizontal distance from the building should the base be placed? (tan 70° ≈ 2.75)

Answer: 26 feet

Horizontal distance = vertical height ÷ tan(angle) = 72 ÷ 2.75 ≈ 26 feet.