Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A landscaper needs to estimate the quantity of topsoil. The area to be covered is 120 square feet, and the topsoil needs to be 6 inches deep. If topsoil is sold by the cubic yard, how many cubic yards of topsoil are needed? (1 foot = 12 inches; 1 yard = 3 feet)
- A1.85 cubic yards
- B5.56 cubic yards
- C2.22 cubic yards
- D3.33 cubic yards
Show answer & explanationAnswer & explanation
Correct answer: C. 2.22 cubic yards
First, convert all measurements to a common unit, preferably feet for volume calculation. Depth = 6 inches = 0.5 feet. Volume in cubic feet = Area * Depth = 120 sq ft * 0.5 ft = 60 cubic feet. Next, convert cubic feet to cubic yards. Since 1 yard = 3 feet, then 1 cubic yard = (3 ft)^3 = 27 cubic feet. So, 60 cubic feet / 27 cubic feet/cubic yard = 2.222... cubic yards. Rounded to two decimal places, this is 2.22 cubic yards.
Why the other options are wrong
- A. This might result from an incorrect conversion factor or arithmetic error.
- B. This might result from an error in calculating volume or an incorrect conversion factor for cubic yards.
- D. This might result from dividing by 18 (3*6) instead of 27 for cubic yard conversion.
Volume Unit Conversion
Converting volume units requires cubing the linear conversion factor. For example, if 1 linear unit A = x linear units B, then 1 cubic unit A = x^3 cubic units B.
- Volume = Length * Width * Height (or Area * Height).
- 1 foot = 12 inches, so 1 cubic foot = 1728 cubic inches.
- 1 yard = 3 feet, so 1 cubic yard = 27 cubic feet.
- Ensure all dimensions are in the same linear unit before calculating volume.
Memory trick: Same unit first, then cube the conversion, for volume's true version!