By Lisa Maloney, Updated Aug 30, 2022
eyjafjallajokull/iStock/GettyImages
Ever wondered how everyday math applies to real‑world tasks? Picture your aunt planning a garden and needing a specific volume of topsoil. She tells you the cubic yards required and asks for the total weight in tons. By knowing the volume and the weight per cubic yard, you can give her a quick, reliable answer.
First, measure or obtain the volume of the space you’ll fill with soil. If the dimensions are already in cubic yards, you can skip to the next step.
When you’re given linear measurements—say a garden bed that is 1 yd × 3 yd × 1/5 yd deep—you multiply them to obtain the cubic yardage:
1 yd × 3 yd × 1/5 yd = 3/5 yd³
If your measurements are in feet, convert each to yards by dividing by three. For example, a space that is 3 ft × 9 ft × 6 ft becomes:
1 yd × 3 yd × 2 yd = 6 yd³
When given a volume in cubic feet, divide by 27 to get cubic yards. For instance, 54 ft³ equals:
54 ft³ ÷ 27 = 2 yd³
In a classroom setting, the weight per cubic yard might be supplied directly. In real life, you may need to research or contact the supplier. Suppose the wet spring topsoil weighs 1.2 tons per cubic yard.
If the weight is given in pounds—say 2,400 lb per cubic yard—you convert to tons by dividing by 2,000 (short tons). Thus:
2,400 lb ÷ 2,000 = 1.2 tons
In U.S. measurements, a short ton equals 2,000 lb. The British long ton equals 2,240 lb, and the metric ton is 1,000 kg (≈ 2,204.6 lb). Verify which ton type is intended, especially in real‑world contracts or academic problems, to avoid costly mistakes.
With both figures known, simply multiply. Using the earlier example of a 3/5 yd³ bed with soil weighing 1.2 tons/yd³:
3/5 yd³ × 1.2 tons/yd³ = 0.72 tons
Therefore, the topsoil will weigh 0.72 tons.
Unit cancellation works like fraction simplification: yd³ × tons/yd³ yields a result in tons.
