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### Filling a Garden with Topsoil

Date: 2/5/96 at 16:30:8
From: Anonymous
Subject: Math Problem

I have a garden that is 10' x 10' (100 square feet).  I want to add 6"
of topsoil  to my garden.  Topsoil is sold by the cubic yard.  How many
cubic yards of topsoil will I need for my project?  Please give me the
formula to figure this.

Thanks

Date: 2/5/96 at 19:53:7
From: Doctor Ken
Subject: Re: Math Problem

Hello!

The fact that will probably help you most is this: there are 9 square
feet in every square yard, and 27 cubic feet in every cubic yard.  To
see why this is so, look at the following picture:

1 **********************************
*          *          *          *
f *          *          *          *
o *          *          *          *
o *          *          *          *
t *          *          *          *
**********************************
1 *          *          *          *
f *          *          *          *
o *          *          *          *
o *          *          *          *
t *          *          *          *
**********************************
1 *          *          *          *
*          *          *          *
f *          *          *          *
o *          *          *          *
o *          *          *          *
t **********************************
1 foot     1 foot      1 foot

O  N  E     Y  A  R  D

The big square is one yard on a side, and there are nine little squares
inside it, each of which is one square foot.  So there are nine square
feet in one square yard.  If you built a cube that was 1 yard on each
edge, you'd see that you could cut it up into 27 (which is 3 cubed)
smaller squares, each of which measured 1 foot on each side.

-Doctor Ken,  The Math Forum

Date: 2/6/96 at 11:20:11
From: Anonymous
Subject: Re: Math Problem

Thanks for your response to my question.

What I need to know is how to convert the area measurement (square
yards) to the volume measurement (cubic yards) using the above example.
(11.12 square yards to cover with 6" of topsoil would take how many
cubic yards?)

Thanks

Date: 2/6/96 at 14:40:59
From: Doctor Ken
Subject: Re: Math Problem

Hello!

Okay, thanks for the clarification.  The way you get volume units of
anything is to multiply Length x Width x Height, making sure that you're
in the same units with all three dimensions.  So when you have 100
square feet of surface area and you are going to cover it with 6 inches
(that's .5 feet) of topsoil, that amounts to 100 x .5 = 50 cubic feet of
topsoil.  You can then divide by 27 to get the cubic yardage.

-Doctor Ken,  The Math Forum

Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Higher-Dimensional Geometry
High School Practical Geometry
High School Triangles and Other Polygons

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