SOLUTION: 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 depth of
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Question 129752: 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 depth of 1 in, how wide will the border be? Use 3.14 To approximate pi. Express the solution rounded to two decimal places. (1 cubic yard=27 cubic feet) Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website! The pool is a circle with a radius of 7, so the outside edge of border will be a larger circle with a radius of 7 + x, if we let x be the width of the border.
The area of the pool surface is , and the area of the circle described by the outer edge of the border is , so the area of the border would be what is left after you take away the surface area of the pool from the larger circle area:
Since the border is supposed to be 1 inch thick, 1 cubic foot of concrete would cover 12 square feet of border. Since there are 27 cubic feet of concrete, there must be 12 * 27 or 324 square feet of border. Now we can equate this area value to the expression for the area that we developed before.
First we expand and simplify the expression for the area:
Now set this equal to 324
Using 3.14 for , this becomes
From here, just use the quadratic formula (or one of the many quadratic solvers on the web). You will get two answers, but one of them is negative and can be excluded.
