NCCER CORE Construction Math Fundamentals Questions and Answers 1 — Questions and Answers
Question 1: A carpenter needs to cut a piece of wood that is 5 1/8 inches long from a board that is 8 3/4 inches long. After the cut, what is the length of the remaining piece of wood?
- 3 1/2 inches
- 3 5/8 inches (Correct answer)
- 2 1/2 inches
- 3 1/4 inches
Correct answer: 3 5/8 inches
To find the remaining length, subtract the cut length from the original length. First, find a common denominator for the fractions, which is 8. Convert 3/4 to 6/8. The problem becomes 8 6/8 - 5 1/8. Subtract the whole numbers (8 - 5 = 3) and the fractions (6/8 - 1/8 = 5/8). The result is 3 5/8 inches.
Question 2: A construction plan requires a concrete slab with a volume of 3 cubic yards. If the slab is 12 feet long and 9 feet wide, what must be its thickness in inches? (1 cubic yard = 27 cubic feet)
- 6 inches
- 8 inches
- 9 inches (Correct answer)
- 12 inches
Correct answer: 9 inches
First, convert the required volume from cubic yards to cubic feet: 3 cubic yards * 27 cubic feet/yard = 81 cubic feet. Next, calculate the area of the slab: 12 feet * 9 feet = 108 square feet. To find the thickness in feet, divide the volume by the area: 81 cubic feet / 108 square feet = 0.75 feet. Finally, convert the thickness to inches: 0.75 feet * 12 inches/foot = 9 inches.
Question 3: Which of the following is the correct conversion of 6 feet 9 inches to decimal feet?
- 6.50 feet
- 6.90 feet
- 6.75 feet (Correct answer)
- 6.25 feet
Correct answer: 6.75 feet
To convert inches to decimal feet, divide the number of inches by 12. In this case, 9 inches / 12 inches = 0.75. Then, add this decimal value to the whole number of feet. So, 6 feet + 0.75 feet = 6.75 feet.
Question 4: A crew is framing a wall and needs to ensure the corners are perfectly square. They measure 6 feet along one wall from the corner and 8 feet along the adjacent wall from the corner. What should the diagonal measurement between those two points be to confirm a 90-degree angle?
- 9 feet
- 10 feet (Correct answer)
- 12 feet
- 14 feet
Correct answer: 10 feet
This scenario uses the Pythagorean theorem (a² + b² = c²) to verify a right angle. The two wall measurements are the legs of a right triangle (a and b), and the diagonal is the hypotenuse (c). So, 6² + 8² = c². This becomes 36 + 64 = c², which simplifies to 100 = c². The square root of 100 is 10, so the diagonal measurement should be 10 feet. This is a multiple of the common 3-4-5 rule.
Question 5: You are ordering lumber for a project. You need 10 boards, each measuring 2 inches thick, 6 inches wide, and 8 feet long. What is the total number of board feet you need to order?
- 40 board feet
- 60 board feet
- 80 board feet (Correct answer)
- 120 board feet
Correct answer: 80 board feet
The formula for board feet is (Thickness in inches × Width in inches × Length in feet) / 12. For one board: (2" × 6" × 8') / 12 = 96 / 12 = 8 board feet. Since you need 10 boards, multiply the board feet per board by the number of boards: 8 board feet/board × 10 boards = 80 board feet.
Question 6: A cylindrical concrete form for a pillar has a diameter of 2 feet and a height of 10 feet. What is the volume of concrete needed to fill the form, rounded to the nearest cubic foot? (Use π ≈ 3.14)
- 20 cubic feet
- 31 cubic feet (Correct answer)
- 63 cubic feet
- 126 cubic feet
Correct answer: 31 cubic feet
The formula for the volume of a cylinder is V = πr²h. First, find the radius (r) by dividing the diameter by 2: 2 feet / 2 = 1 foot. Then, apply the formula: V = 3.14 × (1 foot)² × 10 feet = 3.14 × 1 square foot × 10 feet = 31.4 cubic feet. Rounded to the nearest cubic foot, the answer is 31 cubic feet.
NCCER CORE Construction Math Fundamentals Questions and Answers 1
A carpenter needs to cut a piece of wood that is 5 1/8 inches long from a board that is 8 3/4 inches long.
After the cut, what is the length of the remaining piece of wood?