Math CentralQuandaries & Queries


Question from Deb, a parent:

Your customer has ordered 67 cubic yards of sand. The inside dimensions of your trailer are 40 feet long by 7 feet wide by 9 feet high. How high must the trailer be filled with sand? (Round up to the nearest inch.)

Hi Deb,

A yard is 3 feet and hence a cube which is 1 yard on each side is 3 feet by 3 feet by 3 feet and hence its volume is 1 cubic yard = $3 \times 3 \times 3 = 27$ cubic feet. Hence your customer has ordered $27 \times 67 = 1809$ cubic feet of sand.

Suppose this amount of sand fills your trailer to a height of $x$ feet. The volume of sand on your trailer is then $40 \times 7 \times x$ cubic feet. But this must be 1809 cubic feet. Solve for $x.$


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