NOCTI Applied Technical Mathematics 2 — Questions and Answers
Question 1: A pipe with an outer diameter of 4 inches has a wall thickness of 0.25 inches. What is the inner diameter?
- 3.5 inches (Correct answer)
- 3.75 inches
- 3.25 inches
- 3.0 inches
Correct answer: 3.5 inches
The inner diameter equals the outer diameter minus twice the wall thickness: 4 - (2 x 0.25) = 4 - 0.5 = 3.5 inches.
When calculating inner diameter from outer diameter and wall thickness, remember that the wall exists on both sides of the pipe. The formula is: ID = OD - 2t. So ID = 4 - 2(0.25) = 4 - 0.5 = 3.5 inches. This calculation is essential in plumbing, HVAC, and piping trades for determining flow capacity and selecting fittings.
Question 2: Convert 3/8 inch to its decimal equivalent.
- 0.250 inches
- 0.375 inches (Correct answer)
- 0.380 inches
- 0.325 inches
Correct answer: 0.375 inches
Divide the numerator by the denominator: 3 divided by 8 = 0.375 inches.
Converting fractions to decimals is a fundamental skill in technical trades. To convert 3/8: divide 3 by 8 = 0.375. Common fractional-decimal equivalents every technician should know: 1/8 = 0.125, 1/4 = 0.250, 3/8 = 0.375, 1/2 = 0.500, 5/8 = 0.625, 3/4 = 0.750, 7/8 = 0.875.
Question 3: What is the area of a circle with a radius of 7 inches? (Use pi approximately equal to 3.14)
- 43.96 square inches
- 153.86 square inches (Correct answer)
- 21.98 square inches
- 307.72 square inches
Correct answer: 153.86 square inches
Area of a circle = pi times r squared = 3.14 x 49 = 153.86 square inches.
The area formula A = pi times r squared is one of the most frequently used calculations in technical trades. With r = 7 inches: A = 3.14 x 49 = 153.86 square inches. This calculation is essential for determining cross-sectional areas of pipes, sizing ductwork, and calculating material needed for circular cuts.
Question 4: A staircase has a total rise of 9 feet. If each riser is 7.5 inches tall, how many risers are needed?
- 12
- 14 (Correct answer)
- 15
- 16
Correct answer: 14
Convert 9 feet to inches: 9 x 12 = 108 inches. Then divide by riser height: 108 divided by 7.5 = 14.4, which rounds to 14 risers.
Stair calculations require converting between units first. Total rise = 9 feet x 12 = 108 inches. Number of risers = 108 / 7.5 = 14.4. Since you cannot have a fractional riser, the standard approach is to use 14 risers and adjust each to exactly 108/14 = 7.714 inches. Building codes typically require risers between 7 and 7-3/4 inches.
Question 5: What is 15% of 240?
- 32
- 36 (Correct answer)
- 40
- 34
Correct answer: 36
15% of 240 = 0.15 x 240 = 36.
Percentage calculations are constant in technical trades. To find 15% of 240: convert 15% to decimal (15 / 100 = 0.15), then multiply (0.15 x 240 = 36). A useful shortcut: 10% of 240 = 24, plus 5% of 240 = 12, totals 36.
Question 6: A rectangular concrete slab measures 12 feet long, 8 feet wide, and 4 inches thick. How many cubic feet of concrete are needed?
- 32 cubic feet (Correct answer)
- 384 cubic feet
- 48 cubic feet
- 128 cubic feet
Correct answer: 32 cubic feet
Convert 4 inches to feet: 4/12 = 0.333 feet. Volume = 12 x 8 x 0.333 = 32 cubic feet.
Volume calculations for concrete require consistent units. Length = 12 ft, Width = 8 ft, Thickness = 4 inches = 4/12 = 0.333 feet. Volume = 12 x 8 x 0.333 = approximately 32 cubic feet. To convert to cubic yards (how concrete is ordered): 32 / 27 = 1.185 cubic yards.
NOCTI Applied Technical Mathematics 2
A pipe with an outer diameter of 4 inches has a wall thickness of 0.25 inches.
What is the inner diameter?