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Filling Cylindrical Holes

Date: 05/18/99 at 13:30:44
From: Daymon Raue
Subject: volume of cylinder

Dear Dr. Math,

I'm filling holes with cement. There are 42 holes they have a 9" 
diameter and are 4' deep. We want to figure out how much cement it 
will take in yards. If you please figure this out and tell me the 
answer, I would appreciate that.

Daymon Raue

Date: 05/18/99 at 16:07:40
From: Doctor Rob
Subject: Re: volume of cylinder

Thanks for writing to Ask Dr. Math!

Each hole has a diameter of 1/4 yard, and so a radius of 1/8 yard,
and a depth of 4/3 yard. The volume of a cylinder is Pi times the
square of the radius, times the depth, so each hole has volume

   V = Pi*(1/8)^2*(4/3) = Pi/48 

or, roughly,

   3.1416/48 = 0.065450 cubic yards.

Now multiply that by the total number of holes -- 42 -- to get 
between 2 and 3 cubic yards, and you're done!

- Doctor Rob, The Math Forum   
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry
High School Practical Geometry

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