Math CentralQuandaries & Queries


Question from Shelia:

I need to level a 18ft x 21ft area that is very uneven. I have used a line level to determine the number of inches at various places in the area. This varies from 1 inch to 15 inches in order to bring the garden area up level. How do I calculate cubic yards so I can order topsoil for the area. If needed, I have the number of inches needed for each square yard area. Thank you for your assistance.

Hi Shelia,

The best you can do is estimate the amount of topsoil needed. The area is 6 yards by 2 yards and I gather from your last sentence that you have a grid of 2 × 6 = 12 square yards and have estimated the average depth of topsoil needed in each of the 12, 1 square yard plots.

Divide each of these 12 depth measurements by 36 to convert it to yards. For each one multiply this depth in yards times the area of the plot (the plots are 1 yd by 1 yd so the area is 1 sq yd) to find the number of cubic yards needed for that plot. Add the 12 results to get the total number of cubic yards needed.

Here is an easier way to do the same thing. Add the 12 depths (in inches) you have and divide the sum by 36 to convert it to yards. Multiply by the area of the plot (again this is just 1 cubic yard) to obtain a cubic yard value which is the (estimated) amount of topsoil needed.

I hope this helps.

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