Math CentralQuandaries & Queries


Question from Carla, a student:

if a pump house that measures 20'x16' sits in the middle of a site that is 50'x60' and you apply crushed rock to the site at depth of 6", how many yards will you need to haul?

Hi Carla,

I am going to imagine that you cover the entire site with 6 inches of rock. There are 3 feet in a yard and 36 inches in a yard so the volume of rock needed to cover the site would be

\[\frac{50}{3} \times \frac{60}{3} \times \frac{6}{36} \mbox{ cubic yards.}\]

Now you want to remove the rock you don't need. That's a solid region, 20 feet by 16 feet and 6 inches deep.


What is the volume of rock you don't need? What is the volume of rock you do need?


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