Plant Operator Selection System Mathematical Usage Problems Flashcards

A cylindrical tank has a diameter of 20 feet and is filled with water to a height of 15 feet. If 1 cubic foot of water is approximately 7.48 gallons, what is the total volume of water in the tank, in gallons?

Answer: 35,238 gallons

First, calculate the volume of the water in cubic feet using the formula for the volume of a cylinder (V = πr²h). The radius (r) is half the diameter (20 feet / 2 = 10 feet). So, V = π * (10 ft)² * 15 ft = 3.14159 * 100 sq ft * 15 ft = 4,712.39 cubic feet. Then, convert cubic feet to gallons: 4,712.39 cubic feet * 7.48 gallons/cubic foot ≈ 35,248.6 gallons. The closest answer is 35,238 gallons.

A pump is designed to move 250 gallons of fluid per minute (GPM). If the pump runs continuously for 3.5 hours, how many gallons of fluid will it move?

Answer: 52,500 gallons

First, convert the run time from hours to minutes: 3.5 hours * 60 minutes/hour = 210 minutes. Then, multiply the total minutes by the pump's flow rate: 210 minutes * 250 GPM = 52,500 gallons.

Two gears in a machine have a size ratio of 5:2. If the larger gear has 90 teeth, how many teeth does the smaller gear have?

Answer: 36 teeth

This is a ratio problem. Set up a proportion: 5/2 = 90/x. To solve for x, cross-multiply: 5 * x = 2 * 90, which simplifies to 5x = 180. Divide both sides by 5 to find x: x = 180 / 5 = 36. The smaller gear has 36 teeth.

A chemical solution needs to be mixed at a concentration of 15%. If the total volume of the final mixture is 200 liters, which of the following calculations correctly determines the volume of chemical required?

Answer: 200 * 0.15

To find a percentage of a number, you must first convert the percentage to a decimal. 15% is equivalent to 0.15 (15 / 100). Then, multiply the total volume by this decimal: 200 liters * 0.15 = 30 liters. The expression 200 * 0.15 correctly represents this calculation.

A rectangular containment basin is 50 meters long, 25 meters wide, and 4 meters deep. If it is 75% full, what is the volume of the liquid in the basin in cubic meters?

Answer: 3,750 cubic meters

First, calculate the total volume of the basin: Volume = length * width * depth = 50 m * 25 m * 4 m = 5,000 cubic meters. Next, calculate 75% of the total volume: 5,000 m³ * 0.75 = 3,750 cubic meters.

An operator needs to solve for X in the equation: 3(X + 4) = 21. What is the value of X?

Answer: 3

First, distribute the 3 on the left side of the equation: 3*X + 3*4 = 21, which simplifies to 3X + 12 = 21. Next, subtract 12 from both sides: 3X = 21 - 12, which gives 3X = 9. Finally, divide both sides by 3: X = 9 / 3 = 3.