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| Math Central | Quandaries & Queries |
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Question from JUDY: IF MY HUSBAND HAS A JOB THAT REQUIRES HIM TO MOVE 50,000 CUBIC YARDS OF DIRT, HOW MUCH LAND WOULD THAT COVER AT 1 FOOT DEPTH. |
Judy,
The volume of dirt in cubic yards is the surface area covered times the depth in yards. Your depth is 1 foot or $\frac{1}{3}$ of a yard so
\[50,000 \mbox{ cubic yards } = \mbox{ surface area } \times \frac13.\]
Thus the surface area he can cover is $50,000 \times 3 = 150,000$ square yards. That's approximately 31 acres.
Penny
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