SOLUTION: 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

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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