NCCER Core Introduction to Construction Math 3 — Questions and Answers
Question 1: How many 16-inch pieces can be cut from an 8-foot board (ignoring blade width)?
- 4 pieces
- 5 pieces
- 6 pieces (Correct answer)
- 8 pieces
Correct answer: 6 pieces
8 feet = 96 inches. 96 / 16 = 6 pieces.
8 ft x 12 = 96 inches. 96 / 16 = 6 pieces. In practice, account for kerf (typically 1/8") per cut. With 5 cuts: 5 x 1/8" = 5/8" lost, still yielding 5 complete pieces with 15-3/8" leftover.
Question 2: What is a board foot?
- A board that is 1 foot long
- A measurement equal to 1" thick x 12" wide x 12" long (Correct answer)
- The weight of one foot of lumber
- A board costing one dollar per foot
Correct answer: A measurement equal to 1" thick x 12" wide x 12" long
A board foot equals 1" x 12" x 12" (144 cubic inches) of lumber volume.
Formula: BF = (Thickness x Width x Length in feet) / 12. Example: a 2" x 6" x 10' board = (2 x 6 x 10) / 12 = 10 board feet. Softwood is sold by linear foot or piece; hardwood is sold by the board foot.
Question 3: What is the circumference of a 6-inch diameter pipe? (Use pi = 3.14)
- 18.84 inches (Correct answer)
- 28.26 inches
- 12.56 inches
- 9.42 inches
Correct answer: 18.84 inches
C = pi x d = 3.14 x 6 = 18.84 inches.
C = pi x d (or 2 x pi x r). Essential for calculating insulation wrap length around pipes, metal needed for round ductwork, and banding material for circular forms. The area formula (A = pi x r^2) gives cross-sectional area for flow capacity.
Question 4: If 2.5 meters approximately equals how many feet? (1 meter = 3.28 feet)
- 6.2 feet
- 7.5 feet
- 8.2 feet (Correct answer)
- 9.8 feet
Correct answer: 8.2 feet
2.5 x 3.28 = 8.2 feet.
Key conversions: 1 meter = 3.281 feet = 39.37 inches, 1 inch = 25.4 mm, 1 foot = 0.3048 meters. Rebar is often metric-sized (#4 = 12.7mm). Many tape measures include both scales.
Question 5: What is the decimal equivalent of 3/16 of an inch?
- 0.1875 inches (Correct answer)
- 0.375 inches
- 0.1625 inches
- 0.25 inches
Correct answer: 0.1875 inches
3 / 16 = 0.1875 inches.
Key equivalents: 1/16 = 0.0625, 1/8 = 0.125, 3/16 = 0.1875, 1/4 = 0.25, 5/16 = 0.3125, 3/8 = 0.375, 7/16 = 0.4375, 1/2 = 0.5. Essential for calculator-to-tape-measure conversion.
Question 6: A room is 12 ft x 15 ft with 8-ft ceilings. What is the volume?
- 1,200 cubic feet
- 1,440 cubic feet (Correct answer)
- 1,800 cubic feet
- 960 cubic feet
Correct answer: 1,440 cubic feet
Volume = 12 x 15 x 8 = 1,440 cubic feet.
V = L x W x H. Room volume is essential for HVAC sizing, ventilation requirements (air changes per hour), and estimating paint quantities. A common HVAC rule: 1 ton of cooling per 400-600 sq ft, but actual calculations consider volume, insulation, and climate.
NCCER Core Introduction to Construction Math 3
How many 16-inch pieces can be cut from an 8-foot board (ignoring blade width)?