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Spreading Mulch on a Garden


Date: 05/15/2000 at 15:44:09
From: Amy 
Subject: Equation with measuring

If there are 4 cubic yards of mulch in a yard, and the mulch is to be 
laid 3 inches thick, how many square feet can you cover? I have no 
idea how to get this answer. Any help at all would be great.

Thank you very much.


Date: 05/15/2000 at 17:13:17
From: Doctor Peterson
Subject: Re: Equation with measuring

Hi, Amy.

Picture the garden full of mulch as a rectangular box, with a base of 
some number X of square feet, and a height of 3 inches. If you change 
the 3 inches to a number of feet, how many cubic feet will there be in 
this "box"? How many cubic feet are there in a 4-cubic-yard bag of 
mulch? (Picture each cubic yard as a 3x3x3-foot box.) Now can you work 
out what X has to be to make these numbers the same?

If you need more help, write back and show me how far you got.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   


Date: 05/15/2000 at 23:54:14
From: Amy
Subject: Re: Equation with measuring

I tried to work the problem, but I'm still stuck. Could I have the 
answer please? Thank you

*This is what I've worked out:

   L = 3ft, W = 3ft, H = 1/3 ft
   36 ft^2 * 1/3 ft


Date: 05/16/2000 at 08:57:33
From: Doctor Peterson
Subject: Re: Equation with measuring

Hi, Amy.

I don't know where you got the 3 feet, and the 1/3 ft and 36 square 
feet are wrong results. Let's start from the beginning.

Here's the problem again:

>If there are 4 cubic yards of mulch in a yard, and the mulch is to 
>be laid 3 inches thick, how many square feet can you cover?

(I took "in a yard" to be a misprint for "in a bag," or something, 
though it could mean we're to spread it out over the yard of a house, 
and are finding out how big the "yard" can be. The use of the word 
"yard" may be confusing you!)

The first thing to do is to take the area covered as an unknown 
variable:

     X = area covered, in square feet

The volume of a box (or any prism) is the product of the base area and 
the height. The height (depth) is 3 inches, or 3/12 = 1/4 foot. So the 
volume of mulch after being spread out over that area is:

     V = 1/4 * X  cubic feet

Now, what is the volume of the mulch originally? It's 4 cubic yards, 
and each cubic yard is a 3 x 3 x 3 foot cube. How many cubic feet does 
this make?

Once you've figured this out, you can write an equation:

     1/4 X = ???

Just solve this for X.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
Middle School Geometry
Middle School Higher-Dimensional Geometry

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