Question 113212: Homework question: A circular pool measures 14 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a dept of 1 inch, how wide will the border be? Use 3.14 to approximate pie. Express your solution rounded to two decimal places. (1 cubic yard=27cubic feet)I would like to see how this is worked out, not just get an answer. Thank you!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! The border is a circular ring. The inside radius of the ring is 7 feet, because the diameter of the pool is 14 feet. Let the width of the border be x, then the outer radius of the walkway ring is x + 7.
If the border was one big circle with no pool in the center, the surface area would be  . But we have to subtract the area represented by the pool in the center, and that area is  .
So the equation for the area of the border is 
Now we need to compute the surface area of the border knowing that it is 1 inch thick and consists of a cubic yard of concrete. First of all, there are 12 X 12 X 12 = 1728 cubic inches in a cubic foot and 27 cubic feet in a cubic yard, so there are 1728 X 27 = 46656 cubic inches in a cubic yard. The volume of the border is just its surface area times its thickness, so since we know the volume to be 46656 cubic inches, we can divide by 1 inch to get 46656 square inches of area. But since the radius measurements are in feet, lets convert the square inches back to square feet. There are 12 X 12 = 144 square inches in a square foot, so there are  square feet of area to the border.
Now we are getting somewhere. We can now write:
I'll leave verification of the arithmetic to you, but you will get two solutions:
5.34 and -19.34. Since we are looking for a length, the negative result is clearly an absurdity, so it can be excluded. The width of the border is then 5.34 feet.
Hope this helps,
John
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