FREE OFAI Mathematical Reasoning and Calculation Questions and Answers

Question 1

A standard 50-foot section of fire hose has an internal diameter of 2.5 inches. Approximately how many gallons of water can this single section of hose hold when fully charged? (Note: 1 foot = 12 inches; 1 gallon ≈ 231 cubic inches)

Accepted Answer

12.8 gallons

Answer

First, convert all units to inches. The length is 50 feet * 12 inches/foot = 600 inches. The radius is half the diameter, which is 2.5 inches / 2 = 1.25 inches. Use the formula for the volume of a cylinder (V = πr²h): V = 3.14159 * (1.25)² * 600 ≈ 2945.2 cubic inches. Finally, convert cubic inches to gallons by dividing by 231: 2945.2 / 231 ≈ 12.75, which rounds to 12.8 gallons.

Question 2

A pumper is drafting from a portable tank to supply an attack line flowing 250 gallons per minute (GPM). The portable tank has a capacity of 2,000 gallons. Assuming the tank is full and the pumper maintains a constant flow rate, how many minutes of water supply are available from the tank?

Accepted Answer

8 minutes

Answer

To determine the duration of the water supply, divide the total volume of the tank by the flow rate. Time = Total Volume / Rate. Time = 2,000 gallons / 250 GPM = 8 minutes.

Question 3

A fire crew lays out 350 feet of 2.5-inch hose. The standard friction loss for this hose at the required flow rate is 12 PSI per 100 feet. What is the total friction loss that the pump operator must account for in this hose lay?

Accepted Answer

42 PSI

Answer

First, determine the number of 100-foot sections in the total hose length: 350 feet / 100 feet = 3.5 sections. Next, multiply the number of sections by the friction loss per section: 3.5 sections * 12 PSI/section = 42 PSI.

Question 4

A Self-Contained Breathing Apparatus (SCBA) cylinder is rated for a maximum pressure of 4500 PSI. Departmental policy states that a cylinder must be taken out of service if it falls below 90% of its rated pressure. What is the minimum pressure this cylinder can have to remain in service?

Accepted Answer

4050 PSI

Answer

To find 90% of the total pressure, multiply the maximum pressure by 0.90. Calculation: 4500 PSI * 0.90 = 4050 PSI. This is the minimum allowable pressure for the cylinder to remain in service.

Question 5

During a training exercise, a firefighter starts with an SCBA pressure of 4300 PSI. After 10 minutes of moderate work, the remaining pressure is 2800 PSI. What was the firefighter's average rate of air consumption in PSI per minute?

Accepted Answer

150 PSI per minute

Answer

First, find the total pressure consumed by subtracting the final pressure from the initial pressure: 4300 PSI - 2800 PSI = 1500 PSI. Then, divide the total pressure consumed by the duration of the activity: 1500 PSI / 10 minutes = 150 PSI per minute.

OFAI - Firefighter Aptitude Test Ontario Practice Test

OFAI - Firefighter Aptitude Test Ontario Practice Test

FREE OFAI Mathematical Reasoning and Calculation Questions and Answers