Math CentralQuandaries & Queries


Question from James:

The first formula for figuring cubic yards of concrete need is length in feet, times width in feet, times depth in actual inches, divided by 320. Such as, 150x 50 feet x 4inches divided by 320 = cubic yards. How and why does this formula work?

Hi James,

If I were to be solving this problem I would first convert all the dimensions to yards. There are 3 feet in a yard and 36 inches in a yard so 150 feet is $\large \frac{150}{3}$ yards, 50 feet is $\large \frac{50}{3}$ yards and 4 inches is $\large \frac{4}{36}$ yards. Thus the volume is

\[\frac{150}{3} \times \frac{50}{3} \times \frac{4}{36} = \frac{150 \times 50 \times 4}{3 \times 3 \times 36} = \frac{150 \times 50 \times 4}{324} \mbox{ cubic yards.}\]

To me this is a much better way to solve the problem. First of all the divisor should be 324 not 320 and secondly I don't have anything new to remember. I already know there are 3 feet in a yard and 36 inches in a yard and the 324 comes from a simple calculation rather than trying to remember yet one more conversion factor.

I hope this helps,

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